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## 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 x and write the resulting 'x =' equation in simplified terms.
Sample answers:   x = -y/5 + 12/5,   x = 4y/3 - 2.

 1.   20 = x + 5y 2.   - 32x = - 4y

### Complexity=10, Mode=1

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

 1.   - 13 = - 7x + y 2.   - 3x + y = 10

### Complexity=5, Mode=2

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

 1.   - 5 = - 2x + 4y 2.   - 5x + 5y = 5

### Complexity=10, Mode=2

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

 1.   24 = 7x - 4y 2.   10x + 4y = 17

### Complexity=5, Mode=3

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

 1.   - 4y - 6 = - 5x + 4y 2.   - 2x + 9 = 2x - 5y

### Complexity=10, Mode=3

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

 1.   - 4x - 7y = - 6x + 24 2.   8x - 10y = 9y + 12

### Complexity=5, Mode=1

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

120 = x + 5y
Solution
20 - 5y = x + 5y - 5y
- 5y + 20 = x

x = - 5y + 20

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

### Complexity=10, Mode=1

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

1- 13 = - 7x + y
Solution
- 13 + 7x = - 7x + y + 7x
7x - 13 = y

y = 7x - 13

2- 3x + y = 10
Solution
- 3x + y + 3x = 10 + 3x
y = 3x + 10

### Complexity=5, Mode=2

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

1- 5 = - 2x + 4y
Solution
- 5 - 4y = - 2x + 4y - 4y
- 4y - 5 = - 2x

Divide by - 2

2- 5x + 5y = 5
Solution
- 5x + 5y - 5y = 5 - 5y
- 5x = - 5y + 5

Divide by - 5

x = y + - 1

x = y - 1

### Complexity=10, Mode=2

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

124 = 7x - 4y
Solution
24 - 7x = 7x - 4y - 7x
- 7x + 24 = - 4y

Divide by - 4

210x + 4y = 17
Solution
10x + 4y - 10x = 17 - 10x
4y = - 10x + 17

Divide by 4

### Complexity=5, Mode=3

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

1- 4y - 6 = - 5x + 4y
Solution
- 4y - 6 + 6 = - 5x + 4y + 6
- 4y = - 5x + 4y + 6

- 4y - 4y = - 5x + 4y + 6 - 4y
- 8y = - 5x + 6

Divide by - 8

2- 2x + 9 = 2x - 5y
Solution
- 2x + 9 - 2x = 2x - 5y - 2x
- 4x + 9 = - 5y

Divide by - 5

### Complexity=10, Mode=3

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

1- 4x - 7y = - 6x + 24
Solution
- 4x - 7y + 7y = - 6x + 24 + 7y
- 4x = - 6x + 7y + 24

- 4x + 6x = - 6x + 7y + 24 + 6x
2x = 7y + 24

Divide by 2