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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)
#ProblemCorrect AnswerYour Answer
1
-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

#ProblemCorrect AnswerYour Answer
2
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)
#ProblemCorrect AnswerYour Answer
1
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

#ProblemCorrect AnswerYour Answer
2
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)
#ProblemCorrect AnswerYour Answer
1
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

#ProblemCorrect AnswerYour Answer
2
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)
#ProblemCorrect AnswerYour Answer
1
- 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

#ProblemCorrect AnswerYour Answer
2
-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)
#ProblemCorrect AnswerYour Answer
1
-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

#ProblemCorrect AnswerYour Answer
2
- 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)
#ProblemCorrect AnswerYour Answer
1
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

#ProblemCorrect AnswerYour Answer
2
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

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