Answer
(3,1)
Work Step by Step
Solve each equation for y, then find and graph 3 points for each equation.
$x-y=2$
$x-y+y-2=2-y-2$
$x-2=y$
$\underline{\ x\ \ \ \ \ \ \ \ \ \ \ x-2\ \ \ \ \ \ \ \ \ \ \ \ \ y\ \ }$
$-1\ \ \ \ \ \ \ -1-2\ \ \ \ \ \ -3$
$\ \ \ 0\ \ \ \ \ \ \ \ \ 0-2\ \ \ \ \ \ \ \ \ -2$
$\ \ \ 5\ \ \ \ \ \ \ \ \ 5-2\ \ \ \ \ \ \ \ \ \ \ \ \ \ 3$
$x+3y=6$
$x+3y-x=6-x$
$3y\div3=(6-x)\div3$
$y=2-\frac{x}{3}$
$\underline{\ x\ \ \ \ \ \ \ \ \ \ \ \ 2-\frac{x}{3}\ \ \ \ \ \ \ \ \ \ y}$
$3\ \ \ \ \ \ \ \ \ \ \ \ \ 2-1\ \ \ \ \ \ \ \ \ \ \ 1$
$0\ \ \ \ \ \ \ \ \ \ \ \ \ 2-0\ \ \ \ \ \ \ \ \ \ \ 2$
$-6\ \ \ \ \ \ \ \ \ 2-(-2)\ \ \,\ \ \ 4$
The lines intersect where x=3 and y=1.
When $x=3, x-2=3-2=1.$
When $x=3, 2-\frac{x}{3}=2-1-1$.
