How do you solve the following system?:  x + 6y = 13 , -2x + 6y = -8

Jun 23, 2016

x = 7, y = 1

Explanation:

First, choose one of the 2 equations.
x + 6y = 13 --eq. 1
-2x + 6y = -8 --eq. 2

For this answer i chose:

x + 6y = 13

the first thing i'm going to do is to isolate the x, transfer 6y to the right side of the equal sign.

Then it becomes:

x = 13 - 6y --eq. 1

*noticed that 6y becomes negative when transferred.

The next step is to substitute x or eq. 1 to eq. 2.

-2x + 6y = -8 becomes:
-2 ( 13 - 6y ) + 6y = -8

Simplify the equation, we get:
-26 + 12y + 6y = -8

combine like terms, then simplify further. We get this:
18y = 18

divide it by -6, the answer is:
y = 1

Now that you've obtained y, you can substitute it to any of the 2 original equations to obtain x.

in this case i input y on eq. 1:

x + 6 ( 1 ) = 13

Simplify further, you'll obtain x:

x + 6 = 13

x = 13 - 6

x = 7

*Note that if you substitute y on eq. 2, the value of x should be the same.

so the final answer is:
x = 7, y = 1