Answer
$(-1,3)$
Please see the graph.
Work Step by Step
Red line: $-x+3y=10$
Blue line: $x+y=2$
$-x+3y=10$
$x+y=2$
$x+y=2$
$x+y-y=2-y$
$x=2-y$
$-x+3y=10$
$-(2-y)+3y=10$
$-2+y+3y=10$
$-2+4y+2=10+2$
$4y=12$
$4y/4=12/4$
$y=3$
$x=2-y$
$x=2-3$
$x=-1$
$(-1,3)$ is the solution of the system.