# How do you solve the following system?:  2x +3y =-5 , -2x -12y = 4

Jan 23, 2016

$2 x + 3 y = - 5. \ldots \ldots \ldots \ldots \ldots . \left(i\right)$
$- 2 x - 12 y = 4. \ldots \ldots \ldots \ldots \ldots \left(i i\right)$

Add $\left(i\right)$ and $\left(i i\right)$

$\implies 2 x - 2 x + 3 y - 12 y = - 5 + 4$
$\implies - 9 y = - 1$

$\implies y = \frac{1}{9}$

Put $y = \frac{1}{9}$ in $\left(i\right)$

$\implies 2 x + 3 \cdot \frac{1}{9} = - 5$

$\implies 2 x + \frac{1}{3} = - 5$

$\implies 6 x + 1 = - 15$
$\implies 6 x = - 16$

$\implies x = - \frac{8}{3}$