# How do you solve the system 8x + 7y = -16  and 6x - 3y = -12?

Jun 18, 2015

 color(red)( x = -2, y=0

#### Explanation:

Solving by elimination :

$8 x + 7 y = - 16$
Multiplying the equation by $3$ :
$\textcolor{red}{24 x} + 21 y = - 48$...................EQUATION $1$

$6 x - 3 y = - 12$
Multiplying the equation by $4$:
$\textcolor{red}{24 x} - 12 y = - 48$ ..................EQUATION $2$
The purpose of this multiplication was to create a common term $24 x$ in both of the equations to enable elimination

Subtracting equation $2$ from $1$
$\textcolor{red}{24 x} + 21 y = - 48$
$- \textcolor{red}{24 x} + 12 y = + 48$
$0 + 33 y = 0$
$y = 0$

Finding $x$
$8 x = - 16 - 7 y$
$8 x = - 16 - 0$
$x = - 2$