Math Practice Problems - System of Equations Addition

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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=5

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

Complexity=10

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

Complexity=13

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

Complexity=14

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

Complexity=15

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

Answers

Complexity=3

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

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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)

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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)

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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)

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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)

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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)

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

Problem

Correct Answer

Your Answer

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

Answer (x,y):

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

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