# How do you solve the following system?:  8x - 2y = - 4 , x + 2y = 6

Apr 13, 2016

The solution is:
$x = \frac{2}{9}$

$y = \frac{26}{9}$

#### Explanation:

$8 x \textcolor{b l u e}{- 2 y} = - 4$..........equation $\left(1\right)$

$x + \textcolor{b l u e}{2 y} = 6$.................equation $\left(2\right)$

Solving by elimination:

Adding equations $\left(1\right)$ and $\left(2\right)$

$8 x \textcolor{b l u e}{\cancel{- 2 y}} = - 4$

$x + \cancel{\textcolor{b l u e}{2 y}} = 6$

$9 x = 2$

$x = \frac{2}{9}$

Finding $y$ by substituting the value $x$ in equation $1$
$8 x \textcolor{b l u e}{- 2 y} = - 4$

$8 \cdot \left(\frac{2}{9}\right) \textcolor{b l u e}{- 2 y} = - 4$

$\frac{16}{9} + 4 = 2 y$

$\frac{16}{9} + \frac{36}{9} = 2 y$

$\frac{52}{9} = 2 y$

$\frac{52}{9 \cdot 2} = y$

$y = \frac{\cancel{52}}{\cancel{18}}$

$y = \frac{26}{9}$