Question

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

Answer 1

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

Answer 2

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