# How do you solve the system using the elimination method for 3x-4y=18 and x+3y=-7?

Mar 22, 2018

$\left(x , y\right) = \left(2 , - 3\right)$
See below for solution by elimination

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 3 x - 4 y = 18$
[2]$\textcolor{w h i t e}{\text{XXX}} x + 3 y = - 7$

If we multiply [2] by $3$ we can generate an equation with the same $x$ coefficient as that in [1]
[3]$\textcolor{w h i t e}{\text{XXX}} 3 x + 9 y = - 21$

We can now eliminate the $x$ term by subtracting [1] from [3]
[4]$\textcolor{w h i t e}{\text{XXX}} 13 y = - 39$

After dividing both sides of [4] by $13$
[5]$\textcolor{w h i t e}{\text{XXX}} y = - 3$

Substituting $\left(- 3\right)$ for $y$ in [2}
[6]$\textcolor{w h i t e}{\text{XXX}} x + 3 \cdot \left(- 3\right) = - 7$

Simplifying
[7]$\textcolor{w h i t e}{\text{XXX}} x - 9 = - 7$

[8]$\textcolor{w h i t e}{\text{XXX}} x = 2$