# How do you solve the following system?: -x -y =-1, x -y = -1

Nov 11, 2015

The solution for the system of equations is
color(blue)(x=0
color(blue)(y=1

#### Explanation:

color(blue)(−x)−y=−1 ....equation $\left(1\right)$
color(blue)(x)−y=−1.........equation $\left(2\right)$

Upon observing the two equations we realize that by adding them we can eliminate color(blue)(x

Solving by elimination

cancelcolor(blue)(−x)−y=−1
cancelcolor(blue)(x)−y=−1

$- 2 y = - 2$

$y = \frac{- 2}{-} 2$

color(blue)(y=1

Now we find $x$ by substituting $y$ in equation $1$

−x−y=−1

−x=−1+y

$x = 1 - y$

$x = 1 - 1$

color(blue)(x=0