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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  

Answers


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.

#ProblemCorrect AnswerYour Answer
120 = x + 5y  
Solution
20 - 5y = x + 5y - 5y
- 5y + 20 = x

x = - 5y + 20

#ProblemCorrect AnswerYour Answer
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.

#ProblemCorrect AnswerYour Answer
1- 13 = - 7x + y  
Solution
- 13 + 7x = - 7x + y + 7x
7x - 13 = y

y = 7x - 13

#ProblemCorrect AnswerYour Answer
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.

#ProblemCorrect AnswerYour Answer
1- 5 = - 2x + 4y  
Solution
- 5 - 4y = - 2x + 4y - 4y
- 4y - 5 = - 2x

Divide by - 2





#ProblemCorrect AnswerYour Answer
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.

#ProblemCorrect AnswerYour Answer
124 = 7x - 4y  
Solution
24 - 7x = 7x - 4y - 7x
- 7x + 24 = - 4y

Divide by - 4





#ProblemCorrect AnswerYour Answer
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.

#ProblemCorrect AnswerYour Answer
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




#ProblemCorrect AnswerYour Answer
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.

#ProblemCorrect AnswerYour Answer
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



#ProblemCorrect AnswerYour Answer
28x - 10y = 9y + 12  
Solution
8x - 10y + 10y = 9y + 12 + 10y
8x = 19y + 12

Divide by 8



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