# How do you solve the system 3x - y = 3 and 2x + y = 2?

Jun 4, 2015

$3 x - \textcolor{b l u e}{y} = 3$.....equation $\left(1\right)$
$2 x + \textcolor{b l u e}{y} = 2$....equation $\left(2\right)$

Adding equation $\left(1\right)$ and $\left(2\right)$ we can eliminate color(blue)(y

$3 x - \cancel{y} = 3$
$2 x + \cancel{y} = 2$
$5 x = 5 , \textcolor{g r e e n}{x} = 1$

Substituting the value of $x$ in equation$\left(1\right)$ to find $y$:
$3 x - y = 3$
$3 x - 3 = y$

 color(green)(y = 3-3.(1) = 0
the solution for the system of equations is:
color(green)(x=1 , y=0