System of Equations Addition Sample Problems

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

If your child needs math practice, click here.

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

Sample Problems For System of Equations Addition

Complexity=3

Solve. Answer in the form (x,y). For example: (-2,3)

1.
-x + 3y = ^-1
x - y = 1
Answer (x,y):

2.
x + y = ^-4
2x + y = ^-7
Answer (x,y):

Complexity=5

Solve. Answer in the form (x,y). For example: (-2,3)

1.
2x - 5y = ^-2
^-3x - y = ^-14
Answer (x,y):

2.
2x - 3y = 4
x - y = 1
Answer (x,y):

Complexity=10

Solve. Answer in the form (x,y). For example: (-2,3)

1.
6x - y = 37
^-7x - 4y = ^-7
Answer (x,y):

2.
10x - 7y = 104
^-9x - 8y = ^-65
Answer (x,y):

Complexity=13

Solve. Answer in the form (x,y). For example: (-2,3)

1.
^-2x - y = ^-23
-x + 2y = 21
Answer (x,y):

2.
-x + 9y = 1
^-8x + y = 79
Answer (x,y):

Complexity=14

Solve. Answer in the form (x,y). For example: (-2,3)

1.
-x - y = 8
^-3x + 2y = ^-41
Answer (x,y):

2.
^-9x + 5y = ^-11
^-2x - y = 25
Answer (x,y):

Complexity=15

Solve. Answer in the form (x,y). For example: (-2,3)

1.
x - y = 0
7x + 5y = 168
Answer (x,y):

2.
2x + 13y = 173
11x - 6y = ^-211
Answer (x,y):

Answers

Complexity=3

Solve. Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

Add the equations to eliminate x.
-x + 3y = ^-1
+ [ x - y = 1 ]
2y = 0

Now solve for y
Divide by 2

y = 0

Now plug value of y into the original first equation
-x + 3(0) = ^-1
-x = ^-1
Multiply by ^-1

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

x = 1

Problem

Correct Answer

Your Answer

x + y = ^-4
2x + y = ^-7

Answer (x,y):

Solution
x + y = ^-4
2x + y = ^-7

Subtract the equations to eliminate y.
x + y = ^-4
- [ 2x + y = ^-7 ]
x + y + ^-2x + -y = 3

Now solve for x
Multiply by ^-1

-x(^-1) = 3(^-1)

x = ^-3

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

Complexity=5

Solve. Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

2x - 5y = ^-2
^-3x - y = ^-14

Answer (x,y):

Solution
2x - 5y = ^-2
^-3x - y = ^-14

Multiply the second equation by 5
2x - 5y = ^-2
^-15x - 5y = ^-70

Subtract the equations to eliminate y.
2x - 5y = ^-2
- [ ^-15x - 5y = ^-70 ]
2x - 5y - (^-15x - 5y) = 68

Now solve for x
Divide by 17

x = 4

Now plug value of x into the original first equation
2(4) - 5y = ^-2
^-5y + 8 = ^-2
^-5y + 8 - 8 = ^-2 - 8
^-5y = ^-10

Divide by ^-5

y = 2

Problem

Correct Answer

Your Answer

2x - 3y = 4
x - y = 1

Answer (x,y):

Solution
2x - 3y = 4
x - y = 1

Multiply the second equation by 2
2x - 3y = 4
2x - 2y = 2

Subtract the equations to eliminate x.
2x - 3y = 4
- [ 2x - 2y = 2 ]
2x - 3y - (2x - 2y) = 2

Now solve for y
Multiply by ^-1

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

y = ^-2

Now plug value of y into the original first equation
2x - 3(^-2) = 4
2x + 6 = 4
2x + 6 - 6 = 4 - 6
2x = ^-2

Divide by 2

x = ^-1

Complexity=10

Solve. Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

6x - y = 37
^-7x - 4y = ^-7

Answer (x,y):

Solution
6x - y = 37
^-7x - 4y = ^-7

Multiply the first equation by 4
24x - 4y = 148
^-7x - 4y = ^-7

Subtract the equations to eliminate y.
24x - 4y = 148
- [ ^-7x - 4y = ^-7 ]
24x - 4y - (^-7x - 4y) = 155

Now solve for x
Divide by 31

x = 5

Now plug value of x into the original first equation
6(5) - y = 37
-y + 30 = 37
-y + 30 - 30 = 37 - 30
-y = 7

Multiply by ^-1

-y(^-1) = 7(^-1)

y = ^-7

Problem

Correct Answer

Your Answer

10x - 7y = 104
^-9x - 8y = ^-65

Answer (x,y):

Solution
10x - 7y = 104
^-9x - 8y = ^-65

Multiply the first equation by 8
Multiply the second equation by 7
80x - 56y = 832
^-63x - 56y = ^-455

Subtract the equations to eliminate y.
80x - 56y = 832
- [ ^-63x - 56y = ^-455 ]
80x - 56y - (^-63x - 56y) = 1287

Now solve for x
Divide by 143

x = 9

Now plug value of x into the original first equation
10(9) - 7y = 104
^-7y + 90 = 104
^-7y + 90 - 90 = 104 - 90
^-7y = 14

Divide by ^-7

y = ^-2

Complexity=13

Solve. Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

^-2x - y = ^-23
-x + 2y = 21

Answer (x,y):

Solution
^-2x - y = ^-23
-x + 2y = 21

Multiply the first equation by 2
^-4x - 2y = ^-46
-x + 2y = 21

Add the equations to eliminate y.
^-4x - 2y = ^-46
+ [ -x + 2y = 21 ]
^-5x = ^-25

Now solve for x
Divide by ^-5

x = 5

Now plug value of x into the original first equation
^-2(5) - y = ^-23
-y - 10 = ^-23
-y - 10 + 10 = ^-23 + 10
-y = ^-13

Multiply by ^-1

-y(^-1) = ^-13(^-1)

y = 13

Problem

Correct Answer

Your Answer

-x + 9y = 1
^-8x + y = 79

Answer (x,y):

Solution
-x + 9y = 1
^-8x + y = 79

Multiply the first equation by 8
^-8x + 72y = 8
^-8x + y = 79

Subtract the equations to eliminate x.
^-8x + 72y = 8
- [ ^-8x + y = 79 ]
^-8x + 72y + 8x + -y = ^-71

Now solve for y
Divide by 71

y = ^-1

Now plug value of y into the original first equation
-x + 9(^-1) = 1
-x - 9 = 1
-x - 9 + 9 = 1 + 9
-x = 10

Multiply by ^-1

-x(^-1) = 10(^-1)

x = ^-10

Complexity=14

Solve. Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

-x - y = 8
^-3x + 2y = ^-41

Answer (x,y):

Solution
-x - y = 8
^-3x + 2y = ^-41

Multiply the first equation by 2
^-2x - 2y = 16
^-3x + 2y = ^-41

Add the equations to eliminate y.
^-2x - 2y = 16
+ [ ^-3x + 2y = ^-41 ]
^-5x = ^-25

Now solve for x
Divide by ^-5

x = 5

Now plug value of x into the original first equation
-(5) - y = 8
-y - 5 = 8
-y - 5 + 5 = 8 + 5
-y = 13

Multiply by ^-1

-y(^-1) = 13(^-1)

y = ^-13

Problem

Correct Answer

Your Answer

^-9x + 5y = ^-11
^-2x - y = 25

Answer (x,y):

Solution
^-9x + 5y = ^-11
^-2x - y = 25

Multiply the second equation by 5
^-9x + 5y = ^-11
^-10x - 5y = 125

Add the equations to eliminate y.
^-9x + 5y = ^-11
+ [ ^-10x - 5y = 125 ]
^-19x = 114

Now solve for x
Divide by ^-19

x = ^-6

Now plug value of x into the original first equation
^-9(^-6) + 5y = ^-11
5y + 54 = ^-11
5y + 54 - 54 = ^-11 - 54
5y = ^-65

Divide by 5

y = ^-13

Complexity=15

Solve. Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

x - y = 0
7x + 5y = 168

Answer (x,y):

Solution
x - y = 0
7x + 5y = 168

Multiply the first equation by 5
5x - 5y = 0
7x + 5y = 168

Add the equations to eliminate y.
5x - 5y = 0
+ [ 7x + 5y = 168 ]
12x = 168

Now solve for x
Divide by 12

x = 14

Now plug value of x into the original first equation
14 - y = 0
-y + 14 = 0
-y + 14 - 14 = 0 - 14
-y = ^-14

Multiply by ^-1

-y(^-1) = ^-14(^-1)

y = 14

Problem

Correct Answer

Your Answer

2x + 13y = 173
11x - 6y = ^-211

Answer (x,y):

Solution
2x + 13y = 173
11x - 6y = ^-211

Multiply the first equation by 11
Multiply the second equation by 2
22x + 143y = 1903
22x - 12y = ^-422

Subtract the equations to eliminate x.
22x + 143y = 1903
- [ 22x - 12y = ^-422 ]
22x + 143y + ^-22x - ^-12y = 2325

Now solve for y
Divide by 155

y = 15

Now plug value of y into the original first equation
2x + 13(15) = 173
2x + 195 = 173
2x + 195 - 195 = 173 - 195
2x = ^-22

Divide by 2

x = ^-11

MathScore.com