# How do you solve 3x-y=9 and 2x+y=1?

Jan 8, 2016

The solution for the system of equations is
color(blue)(x=2,y=-3

#### Explanation:

$3 x - \textcolor{b l u e}{y} = 9$......equation $\left(1\right)$

$2 x + \textcolor{b l u e}{y} = 1$......equation $\left(2\right)$

Solving by elimination

Adding equations $1$ and $2$

$3 x - \cancel{\textcolor{b l u e}{y}} = 9$
$2 x + \cancel{\textcolor{b l u e}{y}} = 1$

$5 x = 10$

$x = \frac{10}{5}$

color(blue)(x=2

Finding $y$ from equation $1$

$3 x - y = 9$

$3 \times 2 - y = 9$

$6 - y = 9$

$6 - 9 = y$

color(blue)(y=-3