solve the following system by substitution 3x-2y=-9 2x+y=1

3x-2y=-9_2x+y=1
Since 2x does not contain the variable to solve for, [ move it to the right-hand side of the equation by subtracting 2x from both sides.
3x-2y=-9_y=-2x+1...
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -2x+1.
3x-2(-2x+1)=-9_y=-2x+1...
Multiply -2 by each term inside the parentheses.
3x+4x-2=-9_y=-2x+1...
Since 3x and 4x are like terms, add 4x to 3x to get 7x.
7x-2=-9_y=-2x+1...
Since -2 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 2

to both sides.
7x=2-9_y=-2x+1...
Subtract 9 from 2 to get -7.
7x=-7_y=-2x+1...
Divide each term in the equation by 7.
(7x)/(7)=-(7)/(7)_y=-2x+1...
Simplify the left-hand side of the equation by canceling the common factors.
x=-(7)/(7)_y=-2x+1...
Simplify the right-hand side of the equation by simplifying each term.
x=-1_y=-2x+1...
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -1.
x=-1_y=-2(-1)+1...
Multiply -2 by each term inside the parentheses.
x=-1_y=2+1...
Add 1 to 2 to get 3.
x=-1....
x=-1 and y=3 is the answer. ]

Expert answered|OxTornado007|Points 6709|

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Asked 2/21/2013 8:15:27 PM

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solve the following system by substitution 3x - 2y
= -9 2x + y = 1

Question

Updated 11/29/2017 8:35:29 AM

2 Answers/Comments

3x - 2y = -9

2x + y = 1

y = -2x + 1

3x - 2(-2x + 1) = -9

3x + 4x - 2 = -9

7x - 2 = -9

7x = -9 + 2

7x = -7

x = -7/7

x = -1

2(-1) + y = 1

-2 + y = 1

y = 1 + 2

y = 3

Solution set: (-1, 3)

2x + y = 1

y = -2x + 1

3x - 2(-2x + 1) = -9

3x + 4x - 2 = -9

7x - 2 = -9

7x = -9 + 2

7x = -7

x = -7/7

x = -1

2(-1) + y = 1

-2 + y = 1

y = 1 + 2

y = 3

Solution set: (-1, 3)

Added 11/29/2017 8:32:43 AM

This answer has been confirmed as correct and helpful.

-6x - y = 1

3x - 4y = 31

(-y = 6x + 1)/(-1)

y = -6x - 1

3x - 4(-6x - 1) = 31

3x + 24x + 4 = 31

27x + 4 = 31

27x = 31 - 4

27x = 27

x = 27/27

x = 1

-6(1) - y = 1

-6 - y = 1

-y = 1 + 6

-y = 7

y = -7

Solution set: (1, -7)

3x - 4y = 31

(-y = 6x + 1)/(-1)

y = -6x - 1

3x - 4(-6x - 1) = 31

3x + 24x + 4 = 31

27x + 4 = 31

27x = 31 - 4

27x = 27

x = 27/27

x = 1

-6(1) - y = 1

-6 - y = 1

-y = 1 + 6

-y = 7

y = -7

Solution set: (1, -7)

Added 11/29/2017 8:35:29 AM

This answer has been confirmed as correct and helpful.

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