System of Equations Addition Sample Problems

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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

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