Answer
$x=70,y=110$
Work Step by Step
Given: $x+y=180$ and $4.50x+8.25y=1222.50$
After plugging first equation in second equation, we have
$4.50(180-y)+8.25y=1222.50 \implies 3.75y=412.50$
or, $y=110$
Now, $x+110=180$
or, $x=180-110=70$
Thus, $x=70,y=110$