# How do solve the following linear system?: 8x = -2y - 10, 3x+ 2y - 3 = 0 ?

Mar 25, 2016

The solution for the system of equations is:
color(green)(x = (-13)/5

color(green)( y = 27/(5)

#### Explanation:

$8 x = - 2 y - 10$
$8 x + \textcolor{b l u e}{2 y} = - 10$ ..............equation $\left(1\right)$

$3 x + 2 y - 3 = 0$
$3 x + \textcolor{b l u e}{2 y} = 3$.......................equation $\left(2\right)$

Solving by elimination.

Subtracting equation $2$ from equation $1$

$8 x + \cancel{\textcolor{b l u e}{2 y}} = - 10$

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

$5 x = - 13$

color(green)(x = (-13)/5

Finding $y$ from equation $1$

$8 x + 2 y = - 10$

$2 y = - 10 - 8 x$

$2 y = - 10 - 8 \cdot \left(- \frac{13}{5}\right)$

$2 y = - 10 + \left(\frac{104}{5}\right)$

$2 y = - \frac{50}{5} + \left(\frac{104}{5}\right)$

$2 y = \frac{54}{5}$

$y = \frac{54}{5 \cdot 2}$

color(green)( y = 27/(5)