# How do you solve the following system?: -5x -y =1, 3x -y = -2

May 15, 2016

The solution for the set of equations is:

color(blue)(x = -3/8

 color(blue)(y = 7/8

#### Explanation:

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

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

Subtracting equation $2$ from $1$:

$- 5 x \cancel{\textcolor{b l u e}{- y}} = 1$

$- 3 x \cancel{\textcolor{b l u e}{+ y}} = + 2$

$- 8 x = 3$

color(blue)(x = -3/8

Finding $y$ from equation $1$

$- 5 x \textcolor{b l u e}{- y} = 1$

$- 5 x - 1 = y$

$- 5 \cdot \textcolor{b l u e}{\left(- \frac{3}{8}\right)} - 1 = y$

$\frac{15}{8} - 1 = y$

$\frac{15}{8} - \frac{8}{8} = y$

$\frac{7}{8} = y$

 color(blue)(y = 7/8