# How do you find the solution of the system of equations 3x - y = 9  and 2x + y = 6 ?

May 6, 2015

We can add the two equations to eliminate $y$

Adding the 2 equations will give us:

$\left(3 x - y\right) + \left(2 x + y\right) = 9 + 6$

$3 x - \cancel{y} + 2 x + \cancel{y} = 15$

$5 x = 15$
$\textcolor{b l u e}{x = 3}$

Substituting this value of $x$ in the first equation we get $y$ :

we are given:
$3 x - y = 9$

$3 \cdot 3 - y = 9$
$9 - y = 9$
$0 = y$

$\textcolor{b l u e}{y = 0}$

The solution to these system of equations is:

color(green)(x = 3 , y = 0