# How do you solve the following system?: -x -3y =5, -3x +4y = -7

Mar 31, 2016

The solution for the system of equations is:
color(green)( x = 1/13

color(green)(y = -22/13

#### Explanation:

$- x - 3 y = 5$ , multiplying by $3$
$\textcolor{b l u e}{- 3 x} - 9 y = 15$......equation $\left(1\right)$

$\textcolor{b l u e}{- 3 x} + 4 y = - 7$......equation $\left(2\right)$

Solving by elimination.

Subtracting equation $\left(2\right)$ from $\left(1\right)$

$\cancel{\textcolor{b l u e}{- 3 x}} - 9 y = 15$

$\cancel{\textcolor{b l u e}{+ 3 x}} - 4 y = + 7$

$- 13 y = 22$

color(green)(y = -22/13

Finding $x$ from equation $1$

$- x - 3 y = 5$

$x = - 3 y - 5$

$x = - 3 \cdot \left(\textcolor{g r e e n}{- \frac{22}{13}}\right) - 5$

$x = \frac{66}{13} - 5$

$x = \frac{66}{13} - \frac{65}{13}$

color(green)( x = 1/13