Answer
$(3,2)$
Please see the graph.
Work Step by Step
Red line: $x+y=5$
Blue line: $x-y=1$
$x+y+(x-y)=5+1$
$2x=6$
$2x/2=6/2$
$x=3$
$x+y=5$
$3+y=5$
$y=2$
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