# How do you solve the following system of equations?: -x – 2y = 12 , 6-7x +y=0?

May 23, 2016

The solution for the system of equations is:
color(blue)(x=0
 color(blue)(y = -6

#### Explanation:

$- x \textcolor{b l u e}{- 2 y} = 12$...............equation $\left(1\right)$

$- 7 x + y = - 6$, multiplying by $2$
$- 14 x + \textcolor{b l u e}{2 y} = - 12$..equation $\left(2\right)$

Solving by elimination:

Adding equations $2$ and $1$:

$- x \cancel{\textcolor{b l u e}{- 2 y}} = 12$
$- 14 x + \cancel{\textcolor{b l u e}{2 y}} = - 12$

$- 15 x = 0$

$x = \frac{0}{- 15}$

color(blue)(x=0

Finding $y$ from equation $\left(2\right)$
$- 7 x + y = - 6$

$y = - 6 + 7 x$

$y = - 6 + 7 \times 0$

$y = - 6 + 0$

 color(blue)(y = -6