# How do you solve the following linear system 4x - y = 5 , 4x + 4y = -4 ?

Nov 17, 2015

$\left(x , y\right) = \left(\frac{4}{5} , - \frac{9}{5}\right)$

#### Explanation:

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

Subtract [2] from [1]
[3]$\textcolor{w h i t e}{\text{XXX}} - 5 y = 9$

Divide [3] by $\left(- 5\right)$
[4]$\textcolor{w h i t e}{\text{XXX}} y = - \frac{9}{5}$

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

Substitute $\left(- \frac{9}{5}\right)$ from [4] for $y$ in [5]
[6]$\textcolor{w h i t e}{\text{XXX}} x - \frac{9}{5} = - 1$

Add $\frac{9}{5}$ to both sides of [6]
[7]$\textcolor{w h i t e}{\text{XXX}} x = \frac{4}{5}$