Math Practice Problems - System of Equations Substitution

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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=5

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Complexity=10

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Complexity=13

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Complexity=14

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Complexity=15

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Answers

Complexity=3

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Problem

Correct Answer

Your Answer

-x + y = ^-1
x + 3y = ^-11

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
-x + y + x = ^-1 + x
y = x - 1

Original Equations
-x + y = ^-1
x + 3y = ^-11

Solving for y in the first equation yields:
y = x - 1

Substitute this into the second equation:
x + 3(x - 1) = ^-11
4x - 3 = ^-11
Now solving for x...
4x - 3 + 3 = ^-11 + 3
4x = ^-8

Divide by 4

x = ^-2

Now plug value of x into the original first equation
^-1 • ^-2 + y = ^-1
2 + y = ^-1
2 + y - 2 = ^-1 - 2
y = ^-3

Answer: (-2,-3)

Problem

Correct Answer

Your Answer

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

First equation solved for y:

Answer (x,y):

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

Divide by 3

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

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 3

11x = 0

Divide by 11

x = 0

Now plug value of x into the original first equation
0 + 3y = 3
3y = 3
Divide by 3

y = 1

Answer: (0,1)

Complexity=5

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Problem

Correct Answer

Your Answer

-x - 2y = ^-5
2x - 3y = ^-18

First equation solved for y:

Answer (x,y):

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

Divide by ^-2

Original Equations
-x - 2y = ^-5
2x - 3y = ^-18

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 2

7x = ^-21

Divide by 7

x = ^-3

Now plug value of x into the original first equation
^-1 • ^-3 - 2y = ^-5
3 - 2y = ^-5
3 - 2y - 3 = ^-5 - 3
^-2y = ^-8

Divide by ^-2

y = 4

Answer: (-3,4)

Problem

Correct Answer

Your Answer

4x + y = 1
x + y = ^-2

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
4x + y - 4x = 1 - 4x
y = ^-4x + 1

Original Equations
4x + y = 1
x + y = ^-2

Solving for y in the first equation yields:
y = ^-4x + 1

Substitute this into the second equation:
x + ^-4x + 1 = ^-2
^-3x + 1 = ^-2
Now solving for x...
^-3x + 1 - 1 = ^-2 - 1
^-3x = ^-3

Divide by ^-3

x = 1

Now plug value of x into the original first equation
4 • 1 + y = 1
4 + y = 1
4 + y - 4 = 1 - 4
y = ^-3

Answer: (1,-3)

Complexity=10

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Problem

Correct Answer

Your Answer

^-8x - y = 32
3x + y = ^-17

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
^-8x - y + 8x = 32 + 8x
-y = 8x + 32

Multiply by ^-1

-y(^-1) = (8x + 32)(^-1)

y = ^-8x + ^-32

y = ^-8x - 32

Original Equations
^-8x - y = 32
3x + y = ^-17

Solving for y in the first equation yields:
y = ^-8x - 32

Substitute this into the second equation:
3x + ^-8x - 32 = ^-17
^-5x - 32 = ^-17
Now solving for x...
^-5x - 32 + 32 = ^-17 + 32
^-5x = 15

Divide by ^-5

x = ^-3

Now plug value of x into the original first equation
^-8 • ^-3 - y = 32
24 - y = 32
24 - y - 24 = 32 - 24
-y = 8

Multiply by ^-1

-y(^-1) = 8 • ^-1

y = ^-8

Answer: (-3,-8)

Problem

Correct Answer

Your Answer

^-9x - 10y = 64
x - y = ^-5

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
^-9x - 10y + 9x = 64 + 9x
^-10y = 9x + 64

Divide by ^-10

Original Equations
^-9x - 10y = 64
x - y = ^-5

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 10

19x = ^-114

Divide by 19

x = ^-6

Now plug value of x into the original first equation
^-9 • ^-6 - 10y = 64
54 - 10y = 64
54 - 10y - 54 = 64 - 54
^-10y = 10

Divide by ^-10

y = ^-1

Answer: (-6,-1)

Complexity=13

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Problem

Correct Answer

Your Answer

x + 2y = 20
-x + 12y = 134

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
x + 2y - x = 20 - x
2y = -x + 20

Divide by 2

Original Equations
x + 2y = 20
-x + 12y = 134

Solving for y in the first equation yields:

Substitute this into the second equation:

^-7x + 120 = 134
Now solving for x...
^-7x + 120 - 120 = 134 - 120
^-7x = 14

Divide by ^-7

x = ^-2

Now plug value of x into the original first equation
^-2 + 2y = 20
^-2 + 2y = 20
^-2 + 2y + 2 = 20 + 2
2y = 22

Divide by 2

y = 11

Answer: (-2,11)

Problem

Correct Answer

Your Answer

9x - 8y = 72
3x + 10y = ^-90

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
9x - 8y - 9x = 72 - 9x
^-8y = ^-9x + 72

Divide by ^-8

Original Equations
9x - 8y = 72
3x + 10y = ^-90

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 4

57x = 0

Divide by 57

x = 0

Now plug value of x into the original first equation
9 • 0 - 8y = 72
^-8y = 72
Divide by ^-8

y = ^-9

Answer: (0,-9)

Complexity=14

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Problem

Correct Answer

Your Answer

x + 2y = ^-5
^-10x - 13y = ^-13

First equation solved for y:

Answer (x,y):

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

Divide by 2

Original Equations
x + 2y = ^-5
^-10x - 13y = ^-13

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 2

^-7x = ^-91

Divide by ^-7

x = 13

Now plug value of x into the original first equation
13 + 2y = ^-5
13 + 2y = ^-5
13 + 2y - 13 = ^-5 - 13
2y = ^-18

Divide by 2

y = ^-9

Answer: (13,-9)

Problem

Correct Answer

Your Answer

3x + 4y = ^-57
10x + 7y = ^-152

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
3x + 4y - 3x = ^-57 - 3x
4y = ^-3x - 57

Divide by 4

Original Equations
3x + 4y = ^-57
10x + 7y = ^-152

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 4

19x = ^-209

Divide by 19

x = ^-11

Now plug value of x into the original first equation
3 • ^-11 + 4y = ^-57
^-33 + 4y = ^-57
^-33 + 4y + 33 = ^-57 + 33
4y = ^-24

Divide by 4

y = ^-6

Answer: (-11,-6)

Complexity=15

Solve by substitution.
In step 1, answer in the form y = mx + b, such as y = 3x + 2 or y = -x/3 - 6.
In step 2, answer in the form (x,y). For example: (-2,3).

Problem

Correct Answer

Your Answer

^-14x - 9y = 41
5x + 7y = ^-26

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
^-14x - 9y + 14x = 41 + 14x
^-9y = 14x + 41

Divide by ^-9

Original Equations
^-14x - 9y = 41
5x + 7y = ^-26

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 9

^-53x = 53

Divide by ^-53

x = ^-1

Now plug value of x into the original first equation
^-14 • ^-1 - 9y = 41
14 - 9y = 41
14 - 9y - 14 = 41 - 14
^-9y = 27

Divide by ^-9

y = ^-3

Answer: (-1,-3)

Problem

Correct Answer

Your Answer

3x + 4y = 18
x - 13y = ^-166

First equation solved for y:

Answer (x,y):

Solution
Solve the first equation for y
3x + 4y - 3x = 18 - 3x
4y = ^-3x + 18

Divide by 4

Original Equations
3x + 4y = 18
x - 13y = ^-166

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 4

43x = ^-430

Divide by 43

x = ^-10

Now plug value of x into the original first equation
3 • ^-10 + 4y = 18
^-30 + 4y = 18
^-30 + 4y + 30 = 18 + 30
4y = 48

Divide by 4

y = 12

Answer: (-10,12)

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