## Two Variable Equations - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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### Complexity=5, Mode=1

Solve for y and write the resulting equation beginning with 'y =' and in simplified terms.
Sample answers: y = -x/5 + 12/5       y = 4x/3 - 2
 1.   - 2x + y = - 10 2.   10 = - 3x + y

### Complexity=10, Mode=1

Solve for x and write the resulting equation beginning with 'x =' and in simplified terms.
Sample answers: x = -y/5 + 12/5       x = 4y/3 - 2
 1.   - 7 = x - 9y 2.   - 32x = - 4y

### Complexity=5, Mode=2

Solve for y and write the resulting equation beginning with 'y =' and in simplified terms.
Sample answers: y = -x/5 + 12/5       y = 4x/3 - 2
 1.   - 6 = - 3x - 2y 2.   - 22 = - 3x + 2y

### Complexity=10, Mode=2

Solve for x and write the resulting equation beginning with 'x =' and in simplified terms.
Sample answers: x = -y/5 + 12/5       x = 4y/3 - 2
 1.   - 13 = 8x + 6y 2.   2x - 4y = - 13

### Complexity=5, Mode=3

Solve for y and write the resulting equation beginning with 'y =' and in simplified terms.
Sample answers: y = -x/5 + 12/5       y = 4x/3 - 2
 1.   - 2x + 2y = - 2y + 22 2.   3x + 5y = - 4y + 11

### Complexity=10, Mode=3

Solve for x and write the resulting equation beginning with 'x =' and in simplified terms.
Sample answers: x = -y/5 + 12/5       x = 4y/3 - 2
 1.   - 3x - 6y = - 2x - 23 2.   - 8y - 18 = 2x - 8y

### Complexity=5, Mode=1

Solve for y and write the resulting equation beginning with 'y =' and in simplified terms.
Sample answers: y = -x/5 + 12/5       y = 4x/3 - 2
1- 2x + y = - 10
Solution
- 2x + y + 2x = - 10 + 2x
y = 2x - 10

210 = - 3x + y
Solution
10 + 3x = - 3x + y + 3x
3x + 10 = y

y = 3x + 10

### Complexity=10, Mode=1

Solve for x and write the resulting equation beginning with 'x =' and in simplified terms.
Sample answers: x = -y/5 + 12/5       x = 4y/3 - 2
1- 7 = x - 9y
Solution
- 7 + 9y = x - 9y + 9y
9y - 7 = x

x = 9y - 7

2- 32x = - 4y
Solution
Divide by - 32

### Complexity=5, Mode=2

Solve for y and write the resulting equation beginning with 'y =' and in simplified terms.
Sample answers: y = -x/5 + 12/5       y = 4x/3 - 2
1- 6 = - 3x - 2y
Solution
- 6 + 3x = - 3x - 2y + 3x
3x - 6 = - 2y

Divide by - 2

2- 22 = - 3x + 2y
Solution
- 22 + 3x = - 3x + 2y + 3x
3x - 22 = 2y

Divide by 2

### Complexity=10, Mode=2

Solve for x and write the resulting equation beginning with 'x =' and in simplified terms.
Sample answers: x = -y/5 + 12/5       x = 4y/3 - 2
1- 13 = 8x + 6y
Solution
- 13 - 6y = 8x + 6y - 6y
- 6y - 13 = 8x

Divide by 8

22x - 4y = - 13
Solution
2x - 4y + 4y = - 13 + 4y
2x = 4y - 13

Divide by 2

### Complexity=5, Mode=3

Solve for y and write the resulting equation beginning with 'y =' and in simplified terms.
Sample answers: y = -x/5 + 12/5       y = 4x/3 - 2
1- 2x + 2y = - 2y + 22
Solution
- 2x + 2y + 2x = - 2y + 22 + 2x
2y = 2x - 2y + 22

2y + 2y = 2x + - 2y + 22 + 2y
4y = 2x + 22

Divide by 4

23x + 5y = - 4y + 11
Solution
3x + 5y - 3x = - 4y + 11 - 3x
5y = - 3x - 4y + 11

5y + 4y = - 3x + - 4y + 11 + 4y
9y = - 3x + 11

Divide by 9

### Complexity=10, Mode=3

Solve for x and write the resulting equation beginning with 'x =' and in simplified terms.
Sample answers: x = -y/5 + 12/5       x = 4y/3 - 2
1- 3x - 6y = - 2x - 23
Solution
- 3x - 6y + 6y = - 2x - 23 + 6y
- 3x = - 2x + 6y - 23

- 3x + 2x = - 2x + 6y + - 23 + 2x
-x = 6y - 23

Multiply by - 1
 -x(- 1) = (6y - 23)(- 1)

x = - 6y - - 23

x = - 6y + 23

2- 8y - 18 = 2x - 8y
Solution
- 8y - 18 + 8y = 2x - 8y + 8y
- 18 = 2x

Divide by 2

- 9 = x

x = - 9