System of Equations Substitution Sample Problems

Math Practice Online > free > lessons > Florida > 8th grade > System of Equations Substitution

If your child needs math practice, click here.

These sample problems below for System of Equations Substitution were generated by the MathScore.com engine.

Sample Problems For System of Equations Substitution

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.	^-3x + y = 6 x + y = ^-2	First equation solved for y: Answer (x,y):
2.	x + 2y = 7 3x - 2y = ^-3	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.	x - y = 1 ^-5x + y = 7	First equation solved for y: Answer (x,y):
2.	4x - y = ^-22 2x - y = ^-12	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.	x + y = 5 5x - 8y = 25	First equation solved for y: Answer (x,y):
2.	x + y = 14 ^-2x - y = ^-18	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.	^-2x - 5y = 53 -x + y = ^-12	First equation solved for y: Answer (x,y):
2.	^-3x - 4y = 19 13x - 9y = 181	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 + 4y = ^-5 ^-4x - y = 20	First equation solved for y: Answer (x,y):
2.	3x + y = ^-6 ^-7x - 5y = 30	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.	^-8x + 9y = 99 13x + 8y = 88	First equation solved for y: Answer (x,y):
2.	^-3x - 5y = ^-77 ^-5x + 6y = 15	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

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

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

Solution
Solve the first equation for y
^-3x + y + 3x = 6 + 3x
y = 3x + 6

Original Equations
^-3x + y = 6
x + y = ^-2

Solving for y in the first equation yields:
y = 3x + 6

Substitute this into the second equation:
x + 3x + 6 = ^-2
4x + 6 = ^-2
Now solving for x...
4x + 6 - 6 = ^-2 - 6
4x = ^-8

Divide by 4

x = ^-2

Now plug value of x into the original first equation
^-3(^-2) + y = 6
6 + y = 6
6 + y - 6 = 6 - 6
y = 0

Answer: (-2,0)

Problem

Correct Answer

Your Answer

x + 2y = 7
3x - 2y = ^-3

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

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

Divide by 2

Original Equations
x + 2y = 7
3x - 2y = ^-3

Solving for y in the first equation yields:

Substitute this into the second equation:

4x - 7 = ^-3
Now solving for x...
4x - 7 + 7 = ^-3 + 7
4x = 4

Divide by 4

x = 1

Now plug value of x into the original first equation
1 + 2y = 7
1 + 2y = 7
1 + 2y - 1 = 7 - 1
2y = 6

Divide by 2

y = 3

Answer: (1,3)

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

x - y = 1
^-5x + y = 7

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

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

Multiply by ^-1

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

y = x + ^-1

y = x - 1

Original Equations
x - y = 1
^-5x + y = 7

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

Substitute this into the second equation:
^-5x + x - 1 = 7
^-4x - 1 = 7
Now solving for x...
^-4x - 1 + 1 = 7 + 1
^-4x = 8

Divide by ^-4

x = ^-2

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

Multiply by ^-1

-y(^-1) = 3(^-1)

y = ^-3

Answer: (-2,-3)

Problem

Correct Answer

Your Answer

4x - y = ^-22
2x - y = ^-12

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

Solution
Solve the first equation for y
4x - y - 4x = ^-22 - 4x
-y = ^-4x - 22

Multiply by ^-1

-y(^-1) = (^-4x - 22)(^-1)

y = 4x - ^-22

y = 4x + 22

Original Equations
4x - y = ^-22
2x - y = ^-12

Solving for y in the first equation yields:
y = 4x + 22

Substitute this into the second equation:
2x - (4x + 22) = ^-12
^-2x - 22 = ^-12
Now solving for x...
^-2x - 22 + 22 = ^-12 + 22
^-2x = 10

Divide by ^-2

x = ^-5

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

Multiply by ^-1

-y(^-1) = ^-2(^-1)

y = 2

Answer: (-5,2)

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

x + y = 5
5x - 8y = 25

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

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

Original Equations
x + y = 5
5x - 8y = 25

Solving for y in the first equation yields:
y = -x + 5

Substitute this into the second equation:
5x - 8(-x + 5) = 25
13x - 40 = 25
Now solving for x...
13x - 40 + 40 = 25 + 40
13x = 65

Divide by 13

x = 5

Now plug value of x into the original first equation
5 + y = 5
5 + y = 5
5 + y - 5 = 5 - 5
y = 0

Answer: (5,0)

Problem

Correct Answer

Your Answer

x + y = 14
^-2x - y = ^-18

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

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

Original Equations
x + y = 14
^-2x - y = ^-18

Solving for y in the first equation yields:
y = -x + 14

Substitute this into the second equation:
^-2x - (-x + 14) = ^-18
-x - 14 = ^-18
Now solving for x...
-x - 14 + 14 = ^-18 + 14
-x = ^-4

Multiply by ^-1

-x(^-1) = ^-4(^-1)

x = 4

Now plug value of x into the original first equation
4 + y = 14
4 + y = 14
4 + y - 4 = 14 - 4
y = 10

Answer: (4,10)

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

^-2x - 5y = 53
-x + y = ^-12

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

Solution
Solve the first equation for y
^-2x - 5y + 2x = 53 + 2x
^-5y = 2x + 53

Divide by ^-5

Original Equations
^-2x - 5y = 53
-x + y = ^-12

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 5

^-7x = ^-7

Divide by ^-7

x = 1

Now plug value of x into the original first equation
^-2(1) - 5y = 53
^-2 - 5y = 53
^-2 - 5y + 2 = 53 + 2
^-5y = 55

Divide by ^-5

y = ^-11

Answer: (1,-11)

Problem

Correct Answer

Your Answer

^-3x - 4y = 19
13x - 9y = 181

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

Solution
Solve the first equation for y
^-3x - 4y + 3x = 19 + 3x
^-4y = 3x + 19

Divide by ^-4

Original Equations
^-3x - 4y = 19
13x - 9y = 181

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 4

79x = 553

Divide by 79

x = 7

Now plug value of x into the original first equation
^-3(7) - 4y = 19
^-21 - 4y = 19
^-21 - 4y + 21 = 19 + 21
^-4y = 40

Divide by ^-4

y = ^-10

Answer: (7,-10)

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 + 4y = ^-5
^-4x - y = 20

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

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

Divide by 4

Original Equations
x + 4y = ^-5
^-4x - y = 20

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 4

^-15x = 75

Divide by ^-15

x = ^-5

Now plug value of x into the original first equation
^-5 + 4y = ^-5
^-5 + 4y = ^-5
^-5 + 4y + 5 = ^-5 + 5
4y = 0

Divide by 4

y = 0

Answer: (-5,0)

Problem

Correct Answer

Your Answer

3x + y = ^-6
^-7x - 5y = 30

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

Solution
Solve the first equation for y
3x + y - 3x = ^-6 - 3x
y = ^-3x - 6

Original Equations
3x + y = ^-6
^-7x - 5y = 30

Solving for y in the first equation yields:
y = ^-3x - 6

Substitute this into the second equation:
^-7x - 5(^-3x - 6) = 30
8x + 30 = 30
Now solving for x...
8x + 30 - 30 = 30 - 30
8x = 0

Divide by 8

x = 0

Now plug value of x into the original first equation
3(0) + y = ^-6
y = ^-6
Answer: (0,-6)

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

^-8x + 9y = 99
13x + 8y = 88

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

Solution
Solve the first equation for y
^-8x + 9y + 8x = 99 + 8x
9y = 8x + 99

Divide by 9

Original Equations
^-8x + 9y = 99
13x + 8y = 88

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 9

181x = 0

Divide by 181

x = 0

Now plug value of x into the original first equation
^-8(0) + 9y = 99
9y = 99
Divide by 9

y = 11

Answer: (0,11)

Problem

Correct Answer

Your Answer

^-3x - 5y = ^-77
^-5x + 6y = 15

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

Solution
Solve the first equation for y
^-3x - 5y + 3x = ^-77 + 3x
^-5y = 3x - 77

Divide by ^-5

Original Equations
^-3x - 5y = ^-77
^-5x + 6y = 15

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 5

^-43x = ^-387

Divide by ^-43

x = 9

Now plug value of x into the original first equation
^-3(9) - 5y = ^-77
^-27 - 5y = ^-77
^-27 - 5y + 27 = ^-77 + 27
^-5y = ^-50

Divide by ^-5

y = 10

Answer: (9,10)

MathScore.com