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## System of Equations Addition - 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. Answer in the form (x,y). For example: (-2,3)

 1.   x + 2y = 42x + y = 5 Answer (x,y): 2.   x + y = - 1- 3x - 2y = 4 Answer (x,y):

### Complexity=5

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

 1.   -x - 4y = 165x - 3y = - 11 Answer (x,y): 2.   - 2x + y = 13- 4x - y = 11 Answer (x,y):

### Complexity=10

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

 1.   8x + 9y = - 81- 2x - y = 19 Answer (x,y): 2.   - 4x - y = 34- 3x - 7y = 38 Answer (x,y):

### Complexity=13

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

 1.   -x + y = - 4-x - 3y = 36 Answer (x,y): 2.   - 5x - 2y = 6111x - 6y = 1 Answer (x,y):

### Complexity=14

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

 1.   -x + 5y = - 524x + 5y = - 117 Answer (x,y): 2.   - 4x - 5y = 73- 8x + y = 3 Answer (x,y):

### Complexity=15

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

 1.   - 11x + 2y = - 267x - 6y = - 26 Answer (x,y): 2.   3x + 5y = - 897x - 6y = - 31 Answer (x,y):

### Complexity=3

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

1
x + 2y = 4
2x + y = 5

Solution
x + 2y = 4
2x + y = 5

Multiply the second equation by 2
x + 2y = 4
4x + 2y = 10

Subtract the equations to eliminate y.
x + 2y = 4
- [ 4x + 2y = 10 ]
- 3x = - 6

Now solve for x
Divide by - 3

x = 2

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

Divide by 2

y = 1

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

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

Multiply the first equation by 2
2x + 2y = - 2
- 3x - 2y = 4

Add the equations to eliminate y.
2x + 2y = - 2
+ [ - 3x - 2y = 4 ]
-x = 2

Now solve for x
Multiply by - 1
 -x(- 1) = 2 • - 1

x = - 2

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

### Complexity=5

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

1
-x - 4y = 16
5x - 3y = - 11

Solution
-x - 4y = 16
5x - 3y = - 11

Multiply the first equation by 5
- 5x - 20y = 80
5x - 3y = - 11

Add the equations to eliminate x.
- 5x - 20y = 80
+ [ 5x - 3y = - 11 ]
- 23y = 69

Now solve for y
Divide by - 23

y = - 3

Now plug value of y into the original first equation
-x - 4 • - 3 = 16
-x + 12 = 16
-x + 12 - 12 = 16 - 12
-x = 4

Multiply by - 1
 -x(- 1) = 4 • - 1

x = - 4

2
- 2x + y = 13
- 4x - y = 11

Solution
- 2x + y = 13
- 4x - y = 11

Add the equations to eliminate y.
- 2x + y = 13
+ [ - 4x - y = 11 ]
- 6x = 24

Now solve for x
Divide by - 6

x = - 4

Now plug value of x into the original first equation
- 2 • - 4 + y = 13
y + 8 = 13
y + 8 - 8 = 13 - 8
y = 5

### Complexity=10

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

1
8x + 9y = - 81
- 2x - y = 19

Solution
8x + 9y = - 81
- 2x - y = 19

Multiply the second equation by 4
8x + 9y = - 81
- 8x - 4y = 76

Add the equations to eliminate x.
8x + 9y = - 81
+ [ - 8x - 4y = 76 ]
5y = - 5

Now solve for y
Divide by 5

y = - 1

Now plug value of y into the original first equation
8x + 9 • - 1 = - 81
8x - 9 = - 81
8x - 9 + 9 = - 81 + 9
8x = - 72

Divide by 8

x = - 9

2
- 4x - y = 34
- 3x - 7y = 38

Solution
- 4x - y = 34
- 3x - 7y = 38

Multiply the first equation by 7
- 28x - 7y = 238
- 3x - 7y = 38

Subtract the equations to eliminate y.
- 28x - 7y = 238
- [ - 3x - 7y = 38 ]
- 25x = 200

Now solve for x
Divide by - 25

x = - 8

Now plug value of x into the original first equation
- 4 • - 8 - y = 34
-y + 32 = 34
-y + 32 - 32 = 34 - 32
-y = 2

Multiply by - 1
 -y(- 1) = 2 • - 1

y = - 2

### Complexity=13

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

1
-x + y = - 4
-x - 3y = 36

Solution
-x + y = - 4
-x - 3y = 36

Subtract the equations to eliminate x.
-x + y = - 4
- [ -x - 3y = 36 ]
4y = - 40

Now solve for y
Divide by 4

y = - 10

Now plug value of y into the original first equation
-x + - 10 = - 4
-x - 10 = - 4
-x - 10 + 10 = - 4 + 10
-x = 6

Multiply by - 1
 -x(- 1) = 6 • - 1

x = - 6

2
- 5x - 2y = 61
11x - 6y = 1

Solution
- 5x - 2y = 61
11x - 6y = 1

Multiply the first equation by 3
- 15x - 6y = 183
11x - 6y = 1

Subtract the equations to eliminate y.
- 15x - 6y = 183
- [ 11x - 6y = 1 ]
- 26x = 182

Now solve for x
Divide by - 26

x = - 7

Now plug value of x into the original first equation
- 5 • - 7 - 2y = 61
- 2y + 35 = 61
- 2y + 35 - 35 = 61 - 35
- 2y = 26

Divide by - 2

y = - 13

### Complexity=14

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

1
-x + 5y = - 52
4x + 5y = - 117

Solution
-x + 5y = - 52
4x + 5y = - 117

Subtract the equations to eliminate y.
-x + 5y = - 52
- [ 4x + 5y = - 117 ]
- 5x = 65

Now solve for x
Divide by - 5

x = - 13

Now plug value of x into the original first equation
- 1 • - 13 + 5y = - 52
5y + 13 = - 52
5y + 13 - 13 = - 52 - 13
5y = - 65

Divide by 5

y = - 13

2
- 4x - 5y = 73
- 8x + y = 3

Solution
- 4x - 5y = 73
- 8x + y = 3

Multiply the second equation by 5
- 4x - 5y = 73
- 40x + 5y = 15

Add the equations to eliminate y.
- 4x - 5y = 73
+ [ - 40x + 5y = 15 ]
- 44x = 88

Now solve for x
Divide by - 44

x = - 2

Now plug value of x into the original first equation
- 4 • - 2 - 5y = 73
- 5y + 8 = 73
- 5y + 8 - 8 = 73 - 8
- 5y = 65

Divide by - 5

y = - 13

### Complexity=15

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

1
- 11x + 2y = - 26
7x - 6y = - 26

Solution
- 11x + 2y = - 26
7x - 6y = - 26

Multiply the first equation by 3
- 33x + 6y = - 78
7x - 6y = - 26

Add the equations to eliminate y.
- 33x + 6y = - 78
+ [ 7x - 6y = - 26 ]
- 26x = - 104

Now solve for x
Divide by - 26

x = 4

Now plug value of x into the original first equation
- 11 • 4 + 2y = - 26
2y - 44 = - 26
2y - 44 + 44 = - 26 + 44
2y = 18

Divide by 2

y = 9

2
3x + 5y = - 89
7x - 6y = - 31

Solution
3x + 5y = - 89
7x - 6y = - 31

Multiply the first equation by 7
Multiply the second equation by 3
21x + 35y = - 623
21x - 18y = - 93

Subtract the equations to eliminate x.
21x + 35y = - 623
- [ 21x - 18y = - 93 ]
53y = - 530

Now solve for y
Divide by 53

y = - 10

Now plug value of y into the original first equation
3x + 5 • - 10 = - 89
3x - 50 = - 89
3x - 50 + 50 = - 89 + 50
3x = - 39

Divide by 3

x = - 13