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

Aug 14, 2015

The solutions for the system of equations is
color(blue)(x=3,y=0

#### Explanation:

$x - y = 3$, multiplying this equation by $2$
$2 x - \textcolor{b l u e}{2 y} = 6$.....equation $\left(1\right)$

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

Now, we can solve through elimination as we have the term $\textcolor{b l u e}{2 y}$ common to both equations.

Subtracting equation $2$ from equation $1$

$2 x - \cancel{\textcolor{b l u e}{2 y}} = 6$
$- x + \cancel{\textcolor{b l u e}{2 y}} = - 3$

color(blue)(x=3

Now we substitute the value of $x$ in equation $1$ to find $y$
$x - y = 3$
$x - 3 = y$

 color(blue)(y = 0