# How do solve the following linear system?:  3x + 4y = -2 , x - 3y = 1 ?

May 25, 2016

$x = - 2$
$y = 1$

#### Explanation:

$3 x + 4 y = - 2 \text{ (1)}$
$- 2 x - 3 y = 1 \text{ (2)}$

$\text{expand both sides of equation (1) by 2;}$
$6 x + 8 y = - 4$
$\text{rearranging the equation :" 6x=-4-8y" } \left(3\right)$

$\text{expand both sides of equation 2 by 3;}$
$- 6 x - 9 y = 3$
$\text{rearranging the equation :"6x=-9y-3" } \left(4\right)$

$\text{Both ;the left sides of equations (3) and (4) are equal}$

$\textcolor{red}{6 x} = - 4 - 8 y$
$\textcolor{red}{6 x} = - 9 y - 3$

$\text{The right sides of equations can be written as equal}$

$- 4 - 8 y = - 9 y - 3$

$9 y - 8 y = - 3 + 4$

$y = 1$

$\text{now use (1) or (2)}$

$3 x + 4 \cdot 1 = - 2$
$3 x + 4 = - 2$
$3 x = - 6$
$x = - \frac{6}{3}$
$x = - 2$