System of Equations Substitution Sample Problems

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Sample Problems For System of Equations Substitution

Complexity=3

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	^-3x + y = 6 x + y = ^-2	First equation solved for y: Answer (x,y):
2.	x + 2y = 7 3x - 2y = ^-3	First equation solved for y: Answer (x,y):

Complexity=5

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	x - y = 1 ^-5x + y = 7	First equation solved for y: Answer (x,y):
2.	4x - y = ^-22 2x - y = ^-12	First equation solved for y: Answer (x,y):

Complexity=10

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	x + y = 5 5x - 8y = 25	First equation solved for y: Answer (x,y):
2.	x + y = 14 ^-2x - y = ^-18	First equation solved for y: Answer (x,y):

Complexity=13

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	^-2x - 5y = 53 -x + y = ^-12	First equation solved for y: Answer (x,y):
2.	^-3x - 4y = 19 13x - 9y = 181	First equation solved for y: Answer (x,y):

Complexity=14

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	x + 4y = ^-5 ^-4x - y = 20	First equation solved for y: Answer (x,y):
2.	3x + y = ^-6 ^-7x - 5y = 30	First equation solved for y: Answer (x,y):

Complexity=15

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

1.	^-8x + 9y = 99 13x + 8y = 88	First equation solved for y: Answer (x,y):
2.	^-3x - 5y = ^-77 ^-5x + 6y = 15	First equation solved for y: Answer (x,y):

Answers

Complexity=3

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

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

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-3x + y + 3x = 6 + 3x
y = 3x + 6

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

Solving for y in the first equation yields:
y = 3x + 6

Substitute this into the second equation:
x + 3x + 6 = ^-2
4x + 6 = ^-2
Now solving for x...
4x + 6 - 6 = ^-2 - 6
4x = ^-8

Divide by 4

x = ^-2

Now plug value of x into the original first equation
^-3(^-2) + y = 6
6 + y = 6
6 + y - 6 = 6 - 6
y = 0

Answer: (-2,0)

Problem

Correct Answer

Your Answer

x + 2y = 7
3x - 2y = ^-3

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
x + 2y - x = 7 - x
2y = -x + 7

Divide by 2

Original Equations
x + 2y = 7
3x - 2y = ^-3

Solving for y in the first equation yields:

Substitute this into the second equation:

4x - 7 = ^-3
Now solving for x...
4x - 7 + 7 = ^-3 + 7
4x = 4

Divide by 4

x = 1

Now plug value of x into the original first equation
1 + 2y = 7
1 + 2y = 7
1 + 2y - 1 = 7 - 1
2y = 6

Divide by 2

y = 3

Answer: (1,3)

Complexity=5

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

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

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
x - y - x = 1 - x
-y = -x + 1

Multiply by ^-1

-y(^-1) = (-x + 1)(^-1)

y = x + ^-1

y = x - 1

Original Equations
x - y = 1
^-5x + y = 7

Solving for y in the first equation yields:
y = x - 1

Substitute this into the second equation:
^-5x + x - 1 = 7
^-4x - 1 = 7
Now solving for x...
^-4x - 1 + 1 = 7 + 1
^-4x = 8

Divide by ^-4

x = ^-2

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

Multiply by ^-1

-y(^-1) = 3(^-1)

y = ^-3

Answer: (-2,-3)

Problem

Correct Answer

Your Answer

4x - y = ^-22
2x - y = ^-12

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
4x - y - 4x = ^-22 - 4x
-y = ^-4x - 22

Multiply by ^-1

-y(^-1) = (^-4x - 22)(^-1)

y = 4x - ^-22

y = 4x + 22

Original Equations
4x - y = ^-22
2x - y = ^-12

Solving for y in the first equation yields:
y = 4x + 22

Substitute this into the second equation:
2x - (4x + 22) = ^-12
^-2x - 22 = ^-12
Now solving for x...
^-2x - 22 + 22 = ^-12 + 22
^-2x = 10

Divide by ^-2

x = ^-5

Now plug value of x into the original first equation
4(^-5) - y = ^-22
^-20 - y = ^-22
^-20 - y + 20 = ^-22 + 20
-y = ^-2

Multiply by ^-1

-y(^-1) = ^-2(^-1)

y = 2

Answer: (-5,2)

Complexity=10

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

x + y = 5
5x - 8y = 25

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
x + y - x = 5 - x
y = -x + 5

Original Equations
x + y = 5
5x - 8y = 25

Solving for y in the first equation yields:
y = -x + 5

Substitute this into the second equation:
5x - 8(-x + 5) = 25
13x - 40 = 25
Now solving for x...
13x - 40 + 40 = 25 + 40
13x = 65

Divide by 13

x = 5

Now plug value of x into the original first equation
5 + y = 5
5 + y = 5
5 + y - 5 = 5 - 5
y = 0

Answer: (5,0)

Problem

Correct Answer

Your Answer

x + y = 14
^-2x - y = ^-18

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
x + y - x = 14 - x
y = -x + 14

Original Equations
x + y = 14
^-2x - y = ^-18

Solving for y in the first equation yields:
y = -x + 14

Substitute this into the second equation:
^-2x - (-x + 14) = ^-18
-x - 14 = ^-18
Now solving for x...
-x - 14 + 14 = ^-18 + 14
-x = ^-4

Multiply by ^-1

-x(^-1) = ^-4(^-1)

x = 4

Now plug value of x into the original first equation
4 + y = 14
4 + y = 14
4 + y - 4 = 14 - 4
y = 10

Answer: (4,10)

Complexity=13

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

^-2x - 5y = 53
-x + y = ^-12

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-2x - 5y + 2x = 53 + 2x
^-5y = 2x + 53

Divide by ^-5

Original Equations
^-2x - 5y = 53
-x + y = ^-12

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 5

^-7x = ^-7

Divide by ^-7

x = 1

Now plug value of x into the original first equation
^-2(1) - 5y = 53
^-2 - 5y = 53
^-2 - 5y + 2 = 53 + 2
^-5y = 55

Divide by ^-5

y = ^-11

Answer: (1,-11)

Problem

Correct Answer

Your Answer

^-3x - 4y = 19
13x - 9y = 181

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-3x - 4y + 3x = 19 + 3x
^-4y = 3x + 19

Divide by ^-4

Original Equations
^-3x - 4y = 19
13x - 9y = 181

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 4

79x = 553

Divide by 79

x = 7

Now plug value of x into the original first equation
^-3(7) - 4y = 19
^-21 - 4y = 19
^-21 - 4y + 21 = 19 + 21
^-4y = 40

Divide by ^-4

y = ^-10

Answer: (7,-10)

Complexity=14

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

x + 4y = ^-5
^-4x - y = 20

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
x + 4y - x = ^-5 - x
4y = -x - 5

Divide by 4

Original Equations
x + 4y = ^-5
^-4x - y = 20

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 4

^-15x = 75

Divide by ^-15

x = ^-5

Now plug value of x into the original first equation
^-5 + 4y = ^-5
^-5 + 4y = ^-5
^-5 + 4y + 5 = ^-5 + 5
4y = 0

Divide by 4

y = 0

Answer: (-5,0)

Problem

Correct Answer

Your Answer

3x + y = ^-6
^-7x - 5y = 30

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
3x + y - 3x = ^-6 - 3x
y = ^-3x - 6

Original Equations
3x + y = ^-6
^-7x - 5y = 30

Solving for y in the first equation yields:
y = ^-3x - 6

Substitute this into the second equation:
^-7x - 5(^-3x - 6) = 30
8x + 30 = 30
Now solving for x...
8x + 30 - 30 = 30 - 30
8x = 0

Divide by 8

x = 0

Now plug value of x into the original first equation
3(0) + y = ^-6
y = ^-6
Answer: (0,-6)

Complexity=15

Solve. When solving for y, answer in the form "y=mx+b", such as "y=3x+2" or "y=-x/3-6". Answer in the form (x,y). For example: (-2,3)

Problem

Correct Answer

Your Answer

^-8x + 9y = 99
13x + 8y = 88

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-8x + 9y + 8x = 99 + 8x
9y = 8x + 99

Divide by 9

Original Equations
^-8x + 9y = 99
13x + 8y = 88

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 9

181x = 0

Divide by 181

x = 0

Now plug value of x into the original first equation
^-8(0) + 9y = 99
9y = 99
Divide by 9

y = 11

Answer: (0,11)

Problem

Correct Answer

Your Answer

^-3x - 5y = ^-77
^-5x + 6y = 15

First equation solved for y:
Answer (x,y):

Solution
Solve the first equation for y
^-3x - 5y + 3x = ^-77 + 3x
^-5y = 3x - 77

Divide by ^-5

Original Equations
^-3x - 5y = ^-77
^-5x + 6y = 15

Solving for y in the first equation yields:

Substitute this into the second equation:

Now solving for x...

Multiply by 5

^-43x = ^-387

Divide by ^-43

x = 9

Now plug value of x into the original first equation
^-3(9) - 5y = ^-77
^-27 - 5y = ^-77
^-27 - 5y + 27 = ^-77 + 27
^-5y = ^-50

Divide by ^-5

y = 10

Answer: (9,10)

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