# How do you solve the following system: 2x-y=7, 2x +5y = 5 ?

Dec 22, 2015

$\left(x , y\right) = \left(3 \frac{1}{3} , - \frac{1}{3}\right)$

#### Explanation:

Given:
[1]$\textcolor{w h i t e}{\text{XXX}} 2 x - y = 7$
[2]$\textcolor{w h i t e}{\text{XXX}} 2 x + 5 y = 5$

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

Divide both sides by $\left(- 6\right)$ (and reduce the resulting fraction)
[4]$\textcolor{w h i t e}{\text{XXX}} y = - \frac{1}{3}$

Substitute $\left(- \frac{1}{3}\right)$ for $y$ in [1]
[5]$\textcolor{w h i t e}{\text{XXX}} 2 x - \left(- \frac{1}{3}\right) = 7$

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

Divide both sides by $2$
[7]$\textcolor{w h i t e}{\text{XXX}} x = 3 \frac{1}{3}$