# How do you solve the following linear system:  -2x+5y=4, 4x+5y=-2 ?

Feb 8, 2016

$\left(x , y\right) = \left(- 1 , \frac{2}{5}\right)$

#### Explanation:

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

Subtract [1] from [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 6 x = - 6$

Divide both sides of [3] by $6$
[4]color(white)("XXX"color(green)(x=-1)

Substitute $\left(- 1\right)$ from [4] for $x$ in [1]
[5]$\textcolor{w h i t e}{\text{XXX}} - 2 \times \left(- 1\right) + 5 y = 4$

Simplify [5]
[6]$\textcolor{w h i t e}{\text{XXX}} 5 y = 2$

Divide both sides of [6] by $5$
[7]$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{y = \frac{2}{5}}$