Question

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

2x − 4y = 24
4x − 12y = 36

A x = 18, y = 3
B x = 18, y = −3
C x = −18, y = 3
D x = −18, y = −3

Answer 1

We are going to set it up like this...

`\left[\begin{array}{ccc}2x-4y=24\\4x-12y=36\end{array}\right]`
Let's take the first part...

`2x-4y=24`
Add 4y to both sides.

`2x-4y+4y=24+4y`

`2x=24+4y`
Divide both sides by 2.

`(2x)/(2)=(24+4y)/(2)`

`x=2\left(y+6\right)`
Plug that in.

`\begin{bmatrix}4\cdot \:2\left(y+6\right)-12y=36\end{bmatrix}`

Now we are going to isolate y.

`4\cdot \:2\left(y+6\right)-12y=36`
Simplify.

`8\left(y+6\right)-12y=36`
Expand..

`-4y+48=36`
Subtract 48 from both sides.

`-4y+48-48=36-48`

`-4y=-12`
Divide both sides by -4.

`(-4y)/(-4)=(-12)/(-4)`

`y=3`


`x=2\left(3+6\right)\quad \Rightarrow \quad x=18`
So...
The solutions are...

`y=3,\:x=18`

Have a nice day! :)