# How do you solve 2x - 5y = 11 and 4x + 10y = 18?

Sep 17, 2015

$\left(x , y\right) = \left(5 , - \frac{1}{5}\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXX}} 2 x - 5 y = 11$
[2]$\textcolor{w h i t e}{\text{XXX}} 4 x + 10 y = 18$

Multiply [1] by $2$
[3]$\textcolor{w h i t e}{\text{XXX}} 4 x - 10 y = 22$

Subtract [3] from [2]
[4]$\textcolor{w h i t e}{\text{XXX}} 20 y = - 4$

Divide [4] by $20$
[5]$\textcolor{w h i t e}{\text{XXX}} y = - \frac{1}{5}$

Substitute $\left(- \frac{1}{5}\right)$ for $y$ in [1]
[6]$\textcolor{w h i t e}{\text{XXX}} 2 x - 5 \left(- \frac{1}{5}\right) = 11$

Simplify
[7]$\textcolor{w h i t e}{\text{XXX}} 2 x + 1 = 11$

Subtract $1$
[8]$\textcolor{w h i t e}{\text{XXX}} 2 x = 10$

Divide by $2$
[9]$\textcolor{w h i t e}{\text{XXX}} x = 5$