# How do you solve 6x-2y= - 3 and 5x+3y=4?

Sep 27, 2015

color(blue)(x=-1/28

color(blue)(y=13/6

#### Explanation:

$6 x - 2 y = - 3$, multiplying this equation by $3$

$18 x - \textcolor{b l u e}{6 y} = - 9$.....equation $\left(1\right)$

$5 x + 3 y = 4$, multiplying this equation by$2$

$10 x + \textcolor{b l u e}{6 y} = 8$.......equation $\left(2\right)$

Solving by elimination.
Adding equation $1$ and $2$ to eliminate color(blue)(6y

$18 x - \cancel{\textcolor{b l u e}{6 y}} = - 9$
$10 x + \cancel{\textcolor{b l u e}{6 y}} = 8$

$28 x = - 1$

color(blue)(x=-1/28

Finding $y$ by substituting $x$ in equation $1$

$18 x - 6 y = - 9$

$18 x + 9 = 6 y$

$18 \cdot \left(- \frac{1}{28}\right) + 9 = 6 y$

$- \frac{9}{14} + 9 = 6 y$

$\frac{- 9 + 126}{9} = 6 y$

$\frac{117}{9} = 6 y$

$13 = 6 y$

color(blue)(y=13/6