Math Practice Problems - System of Equations Substitution

System of Equations Substitution - 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=3

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	2x + 3y = ^-4 2x - 3y = ^-4	First equation solved for y: Answer (x,y):
2.	x + 3y = 0 -x - y = ^-2	First equation solved for y: Answer (x,y):

Complexity=5

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	^-3x + 5y = ^-12 4x - y = ^-1	First equation solved for y: Answer (x,y):
2.	3x - 5y = ^-17 x - 5y = ^-9	First equation solved for y: Answer (x,y):

Complexity=10

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	4x + 3y = 37 ^-2x - 3y = ^-29	First equation solved for y: Answer (x,y):
2.	^-2x + 5y = ^-21 3x - 4y = 28	First equation solved for y: Answer (x,y):

Complexity=13

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	^-9x + 7y = ^-122 10x + 13y = ^-93	First equation solved for y: Answer (x,y):
2.	^-6x - 7y = 24 ^-7x + 2y = 28	First equation solved for y: Answer (x,y):

Complexity=14

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	x + y = 20 13x - y = 106	First equation solved for y: Answer (x,y):
2.	2x + y = 27 ^-8x - 7y = ^-129	First equation solved for y: Answer (x,y):

Complexity=15

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	^-6x + 7y = 2 ^-7x - 2y = ^-18	First equation solved for y: Answer (x,y):
2.	^-4x + 5y = ^-45 5x + 2y = 48	First equation solved for y: Answer (x,y):

Answers

Complexity=3

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

2x + 3y = ^-4
2x - 3y = ^-4

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
2x + 3y - 2x = ^-4 - 2x
3y = ^-2x - 4

Divide by 3

Original Equations
2x + 3y = ^-4
2x - 3y = ^-4

Solving for y in the first equation yields:

Substitute this into the second equation:

4x + 4 = ^-4
Now solving for x...
4x + 4 - 4 = ^-4 - 4
4x = ^-8

Divide by 4

x = ^-2

Now plug value of x into the original first equation
2 × ^-2 + 3y = ^-4
^-4 + 3y = ^-4
^-4 + 3y + 4 = ^-4 + 4
3y = 0

Divide by 3

y = 0

Answer: (-2,0)

Problem

Correct Answer

Your Answer

x + 3y = 0
-x - y = ^-2

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
x + 3y - x = 0 - x
3y = -x

Divide by 3

Original Equations
x + 3y = 0
-x - y = ^-2

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...
Multiply by 3

^-2x = ^-6

Divide by ^-2

x = 3

Now plug value of x into the original first equation
3 + 3y = 0
3 + 3y = 0
3 + 3y - 3 = 0 - 3
3y = ^-3

Divide by 3

y = ^-1

Answer: (3,-1)

Complexity=5

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

^-3x + 5y = ^-12
4x - y = ^-1

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-3x + 5y + 3x = ^-12 + 3x
5y = 3x - 12

Divide by 5

Original Equations
^-3x + 5y = ^-12
4x - y = ^-1

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 5

17x = ^-17

Divide by 17

x = ^-1

Now plug value of x into the original first equation
^-3 × ^-1 + 5y = ^-12
3 + 5y = ^-12
3 + 5y - 3 = ^-12 - 3
5y = ^-15

Divide by 5

y = ^-3

Answer: (-1,-3)

Problem

Correct Answer

Your Answer

3x - 5y = ^-17
x - 5y = ^-9

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
3x - 5y - 3x = ^-17 - 3x
^-5y = ^-3x - 17

Divide by ^-5

Original Equations
3x - 5y = ^-17
x - 5y = ^-9

Solving for y in the first equation yields:

Substitute this into the second equation:

^-2x - 17 = ^-9
Now solving for x...
^-2x - 17 + 17 = ^-9 + 17
^-2x = 8

Divide by ^-2

x = ^-4

Now plug value of x into the original first equation
3 × ^-4 - 5y = ^-17
^-12 - 5y = ^-17
^-12 - 5y + 12 = ^-17 + 12
^-5y = ^-5

Divide by ^-5

y = 1

Answer: (-4,1)

Complexity=10

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

4x + 3y = 37
^-2x - 3y = ^-29

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
4x + 3y - 4x = 37 - 4x
3y = ^-4x + 37

Divide by 3

Original Equations
4x + 3y = 37
^-2x - 3y = ^-29

Solving for y in the first equation yields:

Substitute this into the second equation:

2x - 37 = ^-29
Now solving for x...
2x - 37 + 37 = ^-29 + 37
2x = 8

Divide by 2

x = 4

Now plug value of x into the original first equation
4 × 4 + 3y = 37
16 + 3y = 37
16 + 3y - 16 = 37 - 16
3y = 21

Divide by 3

y = 7

Answer: (4,7)

Problem

Correct Answer

Your Answer

^-2x + 5y = ^-21
3x - 4y = 28

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-2x + 5y + 2x = ^-21 + 2x
5y = 2x - 21

Divide by 5

Original Equations
^-2x + 5y = ^-21
3x - 4y = 28

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 5

7x = 56

Divide by 7

x = 8

Now plug value of x into the original first equation
^-2 × 8 + 5y = ^-21
^-16 + 5y = ^-21
^-16 + 5y + 16 = ^-21 + 16
5y = ^-5

Divide by 5

y = ^-1

Answer: (8,-1)

Complexity=13

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

^-9x + 7y = ^-122
10x + 13y = ^-93

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-9x + 7y + 9x = ^-122 + 9x
7y = 9x - 122

Divide by 7

Original Equations
^-9x + 7y = ^-122
10x + 13y = ^-93

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 7

187x = 935

Divide by 187

x = 5

Now plug value of x into the original first equation
^-9 × 5 + 7y = ^-122
^-45 + 7y = ^-122
^-45 + 7y + 45 = ^-122 + 45
7y = ^-77

Divide by 7

y = ^-11

Answer: (5,-11)

Problem

Correct Answer

Your Answer

^-6x - 7y = 24
^-7x + 2y = 28

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-6x - 7y + 6x = 24 + 6x
^-7y = 6x + 24

Divide by ^-7

Original Equations
^-6x - 7y = 24
^-7x + 2y = 28

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 7

^-61x = 244

Divide by ^-61

x = ^-4

Now plug value of x into the original first equation
^-6 × ^-4 - 7y = 24
24 - 7y = 24
24 - 7y - 24 = 24 - 24
^-7y = 0

Divide by ^-7

y = 0

Answer: (-4,0)

Complexity=14

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

x + y = 20
13x - y = 106

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
x + y - x = 20 - x
y = -x + 20

Original Equations
x + y = 20
13x - y = 106

Solving for y in the first equation yields:
y = -x + 20

Substitute this into the second equation:
13x - -x + 20 = 106
14x - 20 = 106
Now solving for x...
14x - 20 + 20 = 106 + 20
14x = 126

Divide by 14

x = 9

Now plug value of x into the original first equation
9 + y = 20
9 + y = 20
9 + y - 9 = 20 - 9
y = 11

Answer: (9,11)

Problem

Correct Answer

Your Answer

2x + y = 27
^-8x - 7y = ^-129

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
2x + y - 2x = 27 - 2x
y = ^-2x + 27

Original Equations
2x + y = 27
^-8x - 7y = ^-129

Solving for y in the first equation yields:
y = ^-2x + 27

Substitute this into the second equation:
^-8x - 7(^-2x + 27) = ^-129
6x - 189 = ^-129
Now solving for x...
6x - 189 + 189 = ^-129 + 189
6x = 60

Divide by 6

x = 10

Now plug value of x into the original first equation
2 × 10 + y = 27
20 + y = 27
20 + y - 20 = 27 - 20
y = 7

Answer: (10,7)

Complexity=15

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

^-6x + 7y = 2
^-7x - 2y = ^-18

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-6x + 7y + 6x = 2 + 6x
7y = 6x + 2

Divide by 7

Original Equations
^-6x + 7y = 2
^-7x - 2y = ^-18

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 7

^-61x = ^-122

Divide by ^-61

x = 2

Now plug value of x into the original first equation
^-6 × 2 + 7y = 2
^-12 + 7y = 2
^-12 + 7y + 12 = 2 + 12
7y = 14

Divide by 7

y = 2

Answer: (2,2)

Problem

Correct Answer

Your Answer

^-4x + 5y = ^-45
5x + 2y = 48

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-4x + 5y + 4x = ^-45 + 4x
5y = 4x - 45

Divide by 5

Original Equations
^-4x + 5y = ^-45
5x + 2y = 48

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 5

33x = 330

Divide by 33

x = 10

Now plug value of x into the original first equation
^-4 × 10 + 5y = ^-45
^-40 + 5y = ^-45
^-40 + 5y + 40 = ^-45 + 40
5y = ^-5

Divide by 5

y = ^-1

Answer: (10,-1)

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