How do you solve the following system?: -8x -5y =13, -7x +y = -2

Dec 26, 2015

The solution for the system of equations is

color(blue)(x=-3/43,y=-107/43

Explanation:

$- 8 x - \textcolor{b l u e}{5 y} = 13$..........equation $\left(1\right)$

$- 7 x + y = - 2$, multiplyting by $5$

$- 35 x + \textcolor{b l u e}{5 y} = - 10$..equation $\left(2\right)$

Solving by elimination.

Adding equations $1$ and $2$

$- 8 x - \cancel{\textcolor{b l u e}{5 y}} = 13$

$- 35 x + \cancel{\textcolor{b l u e}{5 y}} = - 10$

$- 43 x = 3$

color(blue)(x=-3/43

Finding $y$ by substituting $x$ in equation $2$:
$- 7 x + y = - 2$

$- 7 \times \textcolor{b l u e}{\left(- \frac{3}{43}\right)} + y = - 2$

$\frac{21}{43} + y = - 2$

$y = - 2 - \frac{21}{43}$

$y = - \frac{86}{43} - \frac{21}{43}$

color(blue)(y=-107/43