# How do you solve the following system?:  -x+4y=8 , x-5y=4

Dec 22, 2015

The solution for the system of equations is

color(blue)(x=-56, y=-12

#### Explanation:

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

$\textcolor{b l u e}{x} - 5 y = 4$............equation $\left(2\right)$

Solving by elimination:

Adding the two equations would result in an elimination of $x$:

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

$\cancel{\textcolor{b l u e}{x}} - 5 y = 4$

$- y = 12$

color(blue)(y=-12

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

$- x + 4 y = 8$

$4 y - 8 = x$

$- 48 - 8 = x$

$- 56 = x$

color(blue)(x=-56