# How do solve the following linear system?:  -x+5y=-5 , x-2y=8 ?

Nov 26, 2015

The solution for the system of equations is :
color(blue)(x=10,y=1

#### Explanation:

$\textcolor{b l u e}{- x} + 5 y = - 5$........equation $\left(1\right)$

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

We can solve the system of equations through elimination as upon adding the two color( blue)(x gets cancelled.

Adding equations $1$ and $2$:

$\cancel{\textcolor{b l u e}{- x}} + 5 y = - 5$
$\cancel{\textcolor{b l u e}{x}} - 2 y = 8$

$3 y = 3$

$y = \frac{3}{3}$

color(blue)(y=1

Finding $x$ by substituting $y$ in equation $1$:

$- x + 5 y = - 5$

$5 y + 5 = x$

$5 \cdot \textcolor{b l u e}{1} + 5 = x$

$5 + 5 = x$

color(blue)(x=10