Math Practice Problems - Two Variable Equations

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

Answers

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

#	Problem	Correct Answer	Your Answer
1	^-2x + y = ^-10
Solution ^-2x + y + 2x = ^-10 + 2x y = 2x - 10

#	Problem	Correct Answer	Your Answer
2	10 = ^-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

#	Problem	Correct Answer	Your Answer
1	^-7 = x - 9y
Solution ^-7 + 9y = x - 9y + 9y 9y - 7 = x x = 9y - 7

Problem

Correct Answer

Your Answer

^-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

Problem

Correct Answer

Your Answer

^-6 = ^-3x - 2y

Solution
^-6 + 3x = ^-3x - 2y + 3x
3x - 6 = ^-2y

Divide by ^-2

Problem

Correct Answer

Your Answer

^-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

Problem

Correct Answer

Your Answer

^-13 = 8x + 6y

Solution
^-13 - 6y = 8x + 6y - 6y
^-6y - 13 = 8x

Divide by 8

Problem

Correct Answer

Your Answer

2x - 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

Problem

Correct Answer

Your Answer

^-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

Problem

Correct Answer

Your Answer

3x + 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

Problem

Correct Answer

Your Answer

^-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

Problem

Correct Answer

Your Answer

^-8y - 18 = 2x - 8y

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

Divide by 2

^-9 = x

x = ^-9

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