# How do you solve 5x - 4y = 9 and 3 - 2y = -x?

Aug 22, 2015

The solutions are
color(blue)(x=5,y=4

#### Explanation:

$5 x - \textcolor{b l u e}{4 y} = 9$ ......equation $1$

$3 - 2 y = - x$
$- x + 2 y = 3$, multiplying by $2$
$- 2 x + \textcolor{b l u e}{4 y} = 6$.....equation $2$

Solving by elimination
Adding equations $1$ and $2$

$5 x - \cancel{\textcolor{b l u e}{4 y}} = 9$
$- 2 x + \cancel{\textcolor{b l u e}{4 y}} = 6$

$3 x = 15$
color(blue)(x=5

Substituting $x$ in equation $2$ to find $y$
$3 - 2 y = - x$
$3 + x = 2 y$
$3 + 5 = 2 y$
$y = \frac{8}{2}$
color(blue)(y=4