# How do you solve the system of equations: 2x + 5y = 2, -3x - y = -3?

Aug 22, 2015

The solutions are
color(blue)(x=1,y=0

#### Explanation:

$2 x + \textcolor{b l u e}{5 y} = 2$.............equation $1$

$- 3 x - y = - 3$, multiplying this equation by $5$
$- 15 x - \textcolor{b l u e}{5 y} = - 15$....equation $2$

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

$2 x + \cancel{\textcolor{b l u e}{5 y}} = 2$
$- 15 x - \cancel{\textcolor{b l u e}{5 y}} = - 15$

$- 13 x = - 13$
color(blue)(x=1

Finding $y$ from equation $2$
$- 3 x - y = - 3$
$- 3 x + 3 = y$
$- 3 + 3 = y$
color(blue)(y=0