# How do you solve the system of equations: 5x + 3y = 12 ; 4x - 5y = 17?

Aug 22, 2015

The solutions are
color(blue)(y=-1,x=3

#### Explanation:

$5 x + 3 y = 12$, multiplying by $4$
$\textcolor{b l u e}{20 x} + 12 y = 48$....equation $1$

$4 x - 5 y = 17$, multiplying by $5$
$\textcolor{b l u e}{20 x} - 25 y = 85$.....equation $2$

Solving by elimination

Subtracting equation $1$ from $2$

$\cancel{\textcolor{b l u e}{20 x}} + 12 y = 48$
$\cancel{- \textcolor{b l u e}{20 x}} + 25 y = - 85$

$37 y = - 37$
color(blue)(y=-1

Finding $x$ from equation $1$
$5 x + 3 y = 12$

$5 x = 12 - 3 y$

$5 x = 12 + 3$

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