# How do you solve the system of equations: 5x + y = 1, 3x + 2y = 2?

Aug 15, 2015

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

#### Explanation:

$5 x + y = 1$, multiplying this equation by $2$
$10 x + \textcolor{b l u e}{2 y} = 2$........equation $1$

$3 x + \textcolor{b l u e}{2 y} = 2$..........equation $2$

Solving by elimination

Subtracting equation $2$ from $1$ results in elimination of color(blue)(2y

$10 x + \cancel{\textcolor{b l u e}{2 y}} = 2$
$- 3 x - \cancel{\textcolor{b l u e}{2 y}} = - 2$

$7 x = 0$
color(blue)(x=0

Finding $y$ from equation $1$
$5 x + y = 1$
$y = 1 - 5 x$
$y = 1 - 5 \cdot 0$
color(blue)(y=1