Solve the following system of equations by substitution and select the correct answer below:

6x - 4y = 36

2x - 8y = 32

x = 4, y = 3

x = 4, y = - 3

x = - 4, y = 3

x = - 4, y = - 3

The answer is x = 4 and y = - 3

6x-4y=36 - - (1)

2x-8y=32 - (2)

from (1)

-4y = 36-6x

y = - 9+3/2x

(3) into (2)

2x-8 (-9+3/2x) = 32

2x+72-12x=32

72-10x=32

-10x = - 40

x = 4

sub x=4 into y = - 9+3/2x

y = - 9+3/2 (4)

y = - 3

First, we take one of our equations and solve for one variable in terms of the other.

This is similar to solving a one-variable equation.

6x - 4y = 36

Get one variable on one side.

6x = 36 + 4y

Divide by 6.

x = 6 + 2/3y

Now, we substitute this value for x in our second equation.

2x - 8y = 32

2 (6 + 2/3y) - 8y = 32

Distribute the 2 ...

12 + 4/3y - 8y = 32

Subtract 12 from each side ...

4/3y - 8y = 20

Multiply everything by 3 to get rid of that fraction.

4y - 24y = 60

-20y = 60

Divide by - 20 ...

y = - 3

Use this value in an earlier equation to find x.

6x - 4y = 36

6x - 4 (-3) = 36

6x + 12 = 36

6x = 24

x = 4