# How do you solve the following linear system:  5x-3y=-14 , x+3y=2 ?

Nov 20, 2015

x=-2
y=4/3

#### Explanation:

$5 \cdot x - 3 \cdot y = - 14$ Equation 1
$x + 3 \cdot y = 2$ Equation 2

Add equation 1 and equation 2 to eliminate y
$5 \cdot x - 3 \cdot y + \left(x + 3 \cdot y\right) = - 14 + 2$
$6 \cdot x = - 12$
$x = - 2$
$x + 3 \cdot y = 2$
$3 \cdot y = 2 - x = 2 - \left(- 2\right) = 4$
$y = \frac{4}{3}$