PA.7A, SEC 1, scaling eqns (50)
Quiz Summary
0 of 50 Questions completed
Questions:
Information
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
Results
Results
0 of 50 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Categories
- Not categorized 0%
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
- 23
- 24
- 25
- 26
- 27
- 28
- 29
- 30
- 31
- 32
- 33
- 34
- 35
- 36
- 37
- 38
- 39
- 40
- 41
- 42
- 43
- 44
- 45
- 46
- 47
- 48
- 49
- 50
- Current
- Review / Skip
- Answered
- Correct
- Incorrect
-
Question 1 of 50
1. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 4x + y = 10
Equation 2: 2x + 3y = 8
Scale both equations appropriately to introduce an 8x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 2 of 50
2. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 4x – y = 3
Equation 2: 2x + 3y = 10
Scale both equations appropriately to introduce an 8x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x - y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 3 of 50
3. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: 15p + 5q = 25
Equation 2: 30p + 10q = 50
Scale both equations appropriately (by dividing) to introduce a 15p term in each equation, ensuring that the value of p remains the same. Write the new equations.
-
p + q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 4 of 50
4. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: 2p – q = 4
Equation 2: 3p + 4q = 15
Scale both equations appropriately to introduce a 12q term in each equation, ensuring that the value of q remains the same. Write the new equations.
-
p + q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 5 of 50
5. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables m and n:
Equation 1: 6m + 3n = 15
Equation 2: m – 2n = 5
Scale both equations appropriately to introduce an 18m term in each equation, ensuring that the value of m remains the same. Write the new equations.
-
m + n =m - n =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 6 of 50
6. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 16x + 24y = 32
Equation 2: 8x + 12y = 16
Scale both equations appropriately (by dividing) to introduce an 8x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 7 of 50
7. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: a – 2b = 2
Equation 2: 4a + b = 10
Scale both equations appropriately to introduce a 4a term in each equation, ensuring that the value of a remains the same. Write the new equations.
-
a - b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 8 of 50
8. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 2a + 5b = 7
Equation 2: 4a – b = 9
Scale both equations appropriately to introduce a 10b term in each equation, ensuring that the value of b remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 9 of 50
9. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 18a + 6b = 12
Equation 2: 6a + 2b = 4
Scale both equations appropriately (by dividing) to introduce a 6a term in each equation, ensuring that the value of a remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 10 of 50
10. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 5x + 5y = 25
Equation 2: x – 2y = 1
Scale both equations appropriately to introduce a 10x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x - y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 11 of 50
11. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: x + 4y = 8
Equation 2: 3x + 2y = 7
Scale both equations appropriately to introduce a 12y term in each equation, ensuring that the value of y remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 12 of 50
12. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 9x + 9y = 36
Equation 2: 3x + 3y = 12
Scale both equations appropriately (by dividing) to introduce a 3x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 13 of 50
13. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 2x + 4y = 12
Equation 2: 3x + 5y = 15
Scale both equations appropriately to introduce a 6x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 14 of 50
14. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables m and n:
Equation 1: 2m + n = 3
Equation 2: 3m + 4n = 12
Scale both equations appropriately to introduce a 4n term in each equation, ensuring that the value of n remains the same. Write the new equations.
-
m + n =m + n =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 15 of 50
15. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: 2p + 3q = 11
Equation 2: 5p – q = 4
Scale both equations appropriately to introduce a 10p term in each equation, ensuring that the value of p remains the same. Write the new equations.
-
p + q =p - q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 16 of 50
16. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables m and n:
Equation 1: 4m + 12n = 24
Equation 2: 8m + 24n = 48
Scale both equations appropriately (by dividing) to introduce a 4m term in each equation, ensuring that the value of m remains the same. Write the new equations.
-
m + n =m + n =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 17 of 50
17. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 4x + 3y = 24
Equation 2: 5x + 2y = 20
Scale both equations appropriately to introduce a 20x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 18 of 50
18. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 4a + 3b = 9
Equation 2: 5a – b = 2
Scale both equations appropriately to introduce a 20a term in each equation, ensuring that the value of a remains the same. Write the new equations.
-
a + b =a - b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 19 of 50
19. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 2x – 5y = 5
Equation 2: 3x + y = 7
Scale both equations appropriately to introduce a 15y term in each equation, ensuring that the value of y remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 20 of 50
20. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: 20p + 10q = 40
Equation 2: 10p + 5q = 20
Scale both equations appropriately (by dividing) to introduce a 10p term in each equation, ensuring that the value of p remains the same. Write the new equations.
-
p + q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 21 of 50
21. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: x + 2y = 6
Equation 2: 2x + 5y = 10
Scale both equations appropriately to introduce a 10x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 22 of 50
22. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 6x + 2y = 8
Equation 2: x + 5y = 10
Scale both equations appropriately to introduce a 30y term in each equation, ensuring that the value of y remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 23 of 50
23. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 4a + 5b = 20
Equation 2: 3a – 2b = 1
Scale both equations appropriately to introduce a 20b term in each equation, ensuring that the value of b remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 24 of 50
24. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: a + 2b = 3
Equation 2: 2a + b = 4
Scale both equations appropriately to introduce a 6a term in each equation, ensuring that the value of a remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 25 of 50
25. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: p – q = 2
Equation 2: 2p + 3q = 7
Scale both equations appropriately to introduce a 4p term in each equation, ensuring that the value of p remains the same. Write the new equations.
-
p - q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 26 of 50
26. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 8x + 12y = 40
Equation 2: 4x + 2y = 10
Scale both equations appropriately (by dividing) to introduce a 4x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 27 of 50
27. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 2x + 3y = 9
Equation 2: x + 2y = 5
Scale both equations appropriately to introduce a 6y term in each equation, ensuring that the value of y remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 28 of 50
28. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 3a + 2b = 10
Equation 2: a + 4b = 9
Scale both equations appropriately to introduce a 12b term in each equation, ensuring that the value of b remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 29 of 50
29. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: 6p + 18q = 36
Equation 2: 3p + 9q = 27
Scale both equations appropriately (by dividing) to introduce a 3p term in each equation, ensuring that the value of p remains the same. Write the new equations.
-
p + q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 30 of 50
30. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: p + 4q = 8
Equation 2: 3p + 2q = 10
Scale both equations appropriately to introduce a 12p term in each equation, ensuring that the value of p remains the same. Write the new equations.
-
p + q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 31 of 50
31. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 3x + 4y = 12
Equation 2: 2x + 3y = 6
Scale both equations appropriately to introduce a 6x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 32 of 50
32. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 12x + 4y = 16
Equation 2: 6x + 2y = 8
Scale both equations appropriately (by dividing) to introduce a 6x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 33 of 50
33. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 2a + 2b = 6
Equation 2: 3a + 4b = 12
Scale both equations appropriately to introduce an 8b term in each equation, ensuring that the value of b remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 34 of 50
34. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables r and s:
Equation 1: 2r + 5s = 10
Equation 2: 4r – s = 3
Scale both equations appropriately to introduce a 20r term in each equation, ensuring that the value of r remains the same. Write the new equations.
-
r + s =r - s =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 35 of 50
35. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 9a + 6b = 15
Equation 2: 3a + 2b = 5
Scale both equations appropriately (by dividing) to introduce a 3a term in each equation, ensuring that the value of a remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 36 of 50
36. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: x + y = 5
Equation 2: 3x + 5y = 15
Scale both equations appropriately to introduce a 15x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 37 of 50
37. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: 3p + 2q = 10
Equation 2: 5p + q = 9
Scale both equations appropriately to introduce a 10q term in each equation, ensuring that the value of q remains the same. Write the new equations.
-
p + q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 38 of 50
38. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 10x + 20y = 30
Equation 2: 5x + 10y = 15
Scale both equations appropriately (by dividing) to introduce a 5x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 39 of 50
39. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables m and n:
Equation 1: 2m + 3n = 6
Equation 2: m + 4n = 10
Scale both equations appropriately to introduce a 12n term in each equation, ensuring that the value of n remains the same. Write the new equations.
-
m + n =m + n =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 40 of 50
40. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: x – y = 3
Equation 2: 4x + y = 7
Scale both equations appropriately to introduce a 4y term in each equation, ensuring that the value of y remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 41 of 50
41. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: 8p + 4q = 20
Equation 2: 4p + 2q = 10
Scale both equations appropriately (by dividing) to introduce a 4p term in each equation, ensuring that the value of p remains the same. Write the new equations.
-
p + q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 42 of 50
42. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 4x + 3y = 24
Equation 2: 5x + 2y = 20
Scale both equations appropriately to introduce a 20x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 43 of 50
43. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: x + 3y = 9
Equation 2: 2x – 4y = 10
Scale both equations appropriately to introduce a 6x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x - y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 44 of 50
44. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 12x + 36y = 48
Equation 2: 6x + 18y = 24
Scale both equations appropriately (by dividing) to introduce a 6x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 45 of 50
45. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 2x + 3y = 6
Equation 2: x + y = 4
Scale both equations appropriately to introduce a 9y term in each equation, ensuring that the value of y remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 46 of 50
46. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 3a + 7b = 14
Equation 2: a – b = 2
Scale both equations appropriately to introduce a 9a term in each equation, ensuring that the value of a remains the same. Write the new equations.
-
a + b =a - b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 47 of 50
47. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 4a + 8b = 12
Equation 2: 2a + 4b = 6
Scale both equations appropriately (by dividing) to introduce a 2a term in each equation, ensuring that the value of a remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 48 of 50
48. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables a and b:
Equation 1: 3a + 5b = 15
Equation 2: a + 2b = 6
Scale both equations appropriately to introduce a 6a term in each equation, ensuring that the value of a remains the same. Write the new equations.
-
a + b =a + b =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 49 of 50
49. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations involve variables p and q:
Equation 1: 5p + 2q = 12
Equation 2: 3p + 4q = 8
Scale both equations appropriately to introduce an 8q term in each equation, ensuring that the value of q remains the same. Write the new equations.
-
p + q =p + q =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
💡 Sometimes, you want to create matching x-terms (the number in front of x) in two equations by multiplying each entire equation.
For instance, consider these new equations:
Equation 1: 4x + 6y = 16
Equation 2: 2x + 3y = 7
You might decide to scale them so each has 8x.
Multiply Equation 1 by 2 to get 8x + 12y = 32.
Multiply Equation 2 by 4 to get 8x + 12y = 28.
Notice, you have not changed the solutions for x or y, only the representation of each equation.
-
-
Question 50 of 50
50. Question
Topic: Scaling equations.
Please have pen and paper handy to show workings out. 📝
The following equations are given:
Equation 1: 14x + 28y = 42
Equation 2: 7x + 35y = 105
Scale both equations appropriately (by dividing) to introduce a 7x term in each equation, ensuring that the value of x remains the same. Write the new equations.
-
x + y =x + y =⌨️ Enter your answers in the fields provided.
CorrectIncorrectHint
✅ Great work on scaling your equations correctly. Keep it up! 💪
💡 Pro tip: Multiplying each term in the equation by the same factor keeps the solution set the same.
💡 Fun fact: This “elimination” method is one of the quickest ways to remove a variable!
-