How do you solve the following system?: -2x+y=1, -x+y=-3

Dec 23, 2015

The solution for the system of equations is
color(blue)(x=-4,y=-7

Explanation:

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

$- x + \textcolor{b l u e}{y} = - 3$....equation $\left(2\right)$

Solving by elimination

Subtracting equation $2$ from $1$

$- 2 x + \cancel{\textcolor{b l u e}{y}} = 1$

$+ x - \cancel{\textcolor{b l u e}{y}} = + 3$

$- x = 4$

color(blue)(x=-4

Finding $y$ by substituting $x$ in equation $1$:
$- 2 x + y = 1$

$- 2 \times \left(- 4\right) + y = 1$

$8 + y = 1$

$y = 1 - 8$

color(blue)(y=-7