# How do you solve -x+y=5 and x-5y=-9?

Sep 9, 2015

The solution for the system of equations is :
color(blue)(x=-4, y=1

#### Explanation:

$\textcolor{b l u e}{- x} + y = 5$.......equation $\left(1\right)$
$\textcolor{b l u e}{x} - 5 y = - 9$....equation $\left(2\right)$

Solving by elimination

Adding the two equations results in elimination of color(blue)(x
$\cancel{\textcolor{b l u e}{- x}} + y = 5$.......equation $\left(1\right)$
$\cancel{\textcolor{b l u e}{x}} - 5 y = - 9$....equation $\left(2\right)$

$- 4 y = - 4$
color(blue)(y=1

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

$- x + y = 5$
$y - 5 = x$
$1 - 5 = x$
color(blue)(x=-4