Math Practice Problems - System of Equations Addition

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 - 3y = 6
3x + y = ^-2
Answer (x,y):

2.
x + y = 2
-x + y = 0
Answer (x,y):

Complexity=5

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

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

2.
5x - 2y = 7
^-4x - 5y = 1
Answer (x,y):

Complexity=10

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

1.
^-8x + 5y = ^-3
^-4x - 9y = 79
Answer (x,y):

2.
^-7x - 8y = 1
^-2x + 5y = ^-7
Answer (x,y):

Complexity=13

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

1.
5x - 6y = 5
9x + 13y = 247
Answer (x,y):

2.
^-2x - y = 2
x + 6y = 65
Answer (x,y):

Complexity=14

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

1.
^-11x + y = 76
^-7x + 6y = 43
Answer (x,y):

2.
^-8x - 5y = 66
^-12x - y = 34
Answer (x,y):

Complexity=15

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

1.
^-11x - 15y = 338
3x + y = ^-52
Answer (x,y):

2.
3x - 8y = ^-11
4x + 5y = 95
Answer (x,y):

Answers

Complexity=3

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

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

Multiply the second equation by 3
x - 3y = 6
9x + 3y = ^-6

Add the equations to eliminate y.
x - 3y = 6
+ [ 9x + 3y = ^-6 ]
10x = 0

Now solve for x
Divide by 10

x = 0

Now plug value of x into the original first equation
0 - 3y = 6
^-3y = 6
Divide by ^-3

y = ^-2

Problem

Correct Answer

Your Answer

x + y = 2
-x + y = 0

Answer (x,y):

Solution
x + y = 2
-x + y = 0

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

Now solve for y
Divide by 2

y = 1

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

Complexity=5

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

Problem

Correct Answer

Your Answer

x - y = 3
x + 5y = ^-3

Answer (x,y):

Solution
x - y = 3
x + 5y = ^-3

Subtract the equations to eliminate x.
x - y = 3
- [ x + 5y = ^-3 ]
^-6y = 6

Now solve for y
Divide by ^-6

y = ^-1

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

Problem

Correct Answer

Your Answer

5x - 2y = 7
^-4x - 5y = 1

Answer (x,y):

Solution
5x - 2y = 7
^-4x - 5y = 1

Multiply the first equation by 5
Multiply the second equation by 2
25x - 10y = 35
^-8x - 10y = 2

Subtract the equations to eliminate y.
25x - 10y = 35
- [ ^-8x - 10y = 2 ]
33x = 33

Now solve for x
Divide by 33

x = 1

Now plug value of x into the original first equation
5 × 1 - 2y = 7
^-2y + 5 = 7
^-2y + 5 - 5 = 7 - 5
^-2y = 2

Divide by ^-2

y = ^-1

Complexity=10

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

Problem

Correct Answer

Your Answer

^-8x + 5y = ^-3
^-4x - 9y = 79

Answer (x,y):

Solution
^-8x + 5y = ^-3
^-4x - 9y = 79

Multiply the second equation by 2
^-8x + 5y = ^-3
^-8x - 18y = 158

Subtract the equations to eliminate x.
^-8x + 5y = ^-3
- [ ^-8x - 18y = 158 ]
23y = ^-161

Now solve for y
Divide by 23

y = ^-7

Now plug value of y into the original first equation
^-8x + 5 × ^-7 = ^-3
^-8x - 35 = ^-3
^-8x - 35 + 35 = ^-3 + 35
^-8x = 32

Divide by ^-8

x = ^-4

Problem

Correct Answer

Your Answer

^-7x - 8y = 1
^-2x + 5y = ^-7

Answer (x,y):

Solution
^-7x - 8y = 1
^-2x + 5y = ^-7

Multiply the first equation by 2
Multiply the second equation by 7
^-14x - 16y = 2
^-14x + 35y = ^-49

Subtract the equations to eliminate x.
^-14x - 16y = 2
- [ ^-14x + 35y = ^-49 ]
^-51y = 51

Now solve for y
Divide by ^-51

y = ^-1

Now plug value of y into the original first equation
^-7x - 8 × ^-1 = 1
^-7x + 8 = 1
^-7x + 8 - 8 = 1 - 8
^-7x = ^-7

Divide by ^-7

x = 1

Complexity=13

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

Problem

Correct Answer

Your Answer

5x - 6y = 5
9x + 13y = 247

Answer (x,y):

Solution
5x - 6y = 5
9x + 13y = 247

Multiply the first equation by 9
Multiply the second equation by 5
45x - 54y = 45
45x + 65y = 1235

Subtract the equations to eliminate x.
45x - 54y = 45
- [ 45x + 65y = 1235 ]
^-119y = ^-1190

Now solve for y
Divide by ^-119

y = 10

Now plug value of y into the original first equation
5x - 6 × 10 = 5
5x - 60 = 5
5x - 60 + 60 = 5 + 60
5x = 65

Divide by 5

x = 13

Problem

Correct Answer

Your Answer

^-2x - y = 2
x + 6y = 65

Answer (x,y):

Solution
^-2x - y = 2
x + 6y = 65

Multiply the second equation by 2
^-2x - y = 2
2x + 12y = 130

Add the equations to eliminate x.
^-2x - y = 2
+ [ 2x + 12y = 130 ]
11y = 132

Now solve for y
Divide by 11

y = 12

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

Divide by ^-2

x = ^-7

Complexity=14

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

Problem

Correct Answer

Your Answer

^-11x + y = 76
^-7x + 6y = 43

Answer (x,y):

Solution
^-11x + y = 76
^-7x + 6y = 43

Multiply the first equation by 6
^-66x + 6y = 456
^-7x + 6y = 43

Subtract the equations to eliminate y.
^-66x + 6y = 456
- [ ^-7x + 6y = 43 ]
^-59x = 413

Now solve for x
Divide by ^-59

x = ^-7

Now plug value of x into the original first equation
^-11 × ^-7 + y = 76
y + 77 = 76
y + 77 - 77 = 76 - 77
y = ^-1

Problem

Correct Answer

Your Answer

^-8x - 5y = 66
^-12x - y = 34

Answer (x,y):

Solution
^-8x - 5y = 66
^-12x - y = 34

Multiply the second equation by 5
^-8x - 5y = 66
^-60x - 5y = 170

Subtract the equations to eliminate y.
^-8x - 5y = 66
- [ ^-60x - 5y = 170 ]
52x = ^-104

Now solve for x
Divide by 52

x = ^-2

Now plug value of x into the original first equation
^-8 × ^-2 - 5y = 66
^-5y + 16 = 66
^-5y + 16 - 16 = 66 - 16
^-5y = 50

Divide by ^-5

y = ^-10

Complexity=15

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

Problem

Correct Answer

Your Answer

^-11x - 15y = 338
3x + y = ^-52

Answer (x,y):

Solution
^-11x - 15y = 338
3x + y = ^-52

Multiply the second equation by 15
^-11x - 15y = 338
45x + 15y = ^-780

Add the equations to eliminate y.
^-11x - 15y = 338
+ [ 45x + 15y = ^-780 ]
34x = ^-442

Now solve for x
Divide by 34

x = ^-13

Now plug value of x into the original first equation
^-11 × ^-13 - 15y = 338
^-15y + 143 = 338
^-15y + 143 - 143 = 338 - 143
^-15y = 195

Divide by ^-15

y = ^-13

Problem

Correct Answer

Your Answer

3x - 8y = ^-11
4x + 5y = 95

Answer (x,y):

Solution
3x - 8y = ^-11
4x + 5y = 95

Multiply the first equation by 4
Multiply the second equation by 3
12x - 32y = ^-44
12x + 15y = 285

Subtract the equations to eliminate x.
12x - 32y = ^-44
- [ 12x + 15y = 285 ]
^-47y = ^-329

Now solve for y
Divide by ^-47

y = 7

Now plug value of y into the original first equation
3x - 8 × 7 = ^-11
3x - 56 = ^-11
3x - 56 + 56 = ^-11 + 56
3x = 45

Divide by 3

x = 15

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