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

Mar 13, 2016

The solution for the system of equations is:
 color(green)(x =3
color(green)(y = -11

#### Explanation:

$- x - y = 8$ , multiplying this equation by $8$
$\textcolor{g r e e n}{- 8 x} - 8 y = 64$..........equation $\left(1\right)$

$\textcolor{g r e e n}{8 x} + 2 y = 2$.................equation $\left(2\right)$

Solving by elimination would result in elimination of the terms $\textcolor{g r e e n}{8 x}$:

$\cancel{\textcolor{g r e e n}{- 8 x}} - 8 y = 64$
$\cancel{\textcolor{g r e e n}{8 x}} + 2 y = 2$

$- 6 y = 66$

$y = \frac{66}{- 6}$

color(green)(y = -11

Finding the value of $x$ from equation $\left(1\right)$:
$- x - y = 8$

$x = - y - 8$

$x = - \textcolor{g r e e n}{\left(- 11\right)} - 8$

$x = 11 - 8$

 color(green)(x =3