# How do you solve the system -2x -8y = 4 and 5x-5y=20?

Aug 8, 2015

$\left(x , y\right) = \left(\frac{26}{5} , - \frac{6}{5}\right)$
Note: As stated in the comments, this question has been modified. If the original intent was correct (2 equations in 4 variables), no solution is possible.

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$- 2 x - 8 y = 4$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$5 x - 5 y = 20$

Simplifying [1] by dividing by $\left(- 2\right)$
[3]$\textcolor{w h i t e}{\text{XXXX}}$$x + 4 y = - 2$
Simplifying [2] by dividing by $5$
[4]$\textcolor{w h i t e}{\text{XXXX}}$$x - y = 4$

Subtract [4] from [3]
[5]$\textcolor{w h i t e}{\text{XXXX}}$$5 y = - 6$
Divide by $5$
[6]$\textcolor{w h i t e}{\text{XXXX}}$$y = - \frac{6}{5}$

Substituting $\left(- \frac{6}{5}\right)$ for $y$ in [4]
[7]$\textcolor{w h i t e}{\text{XXXX}}$$x - \left(- \frac{6}{5}\right) = 4$

[8]$\textcolor{w h i t e}{\text{XXXX}}$$x = \frac{26}{5}$