Answer
$x=8,y=18$
Work Step by Step
Our constraints are: $x,y\geq0$. Then if we add three times the first and twice the second equation we get: $19\sqrt x=38\sqrt2\\\sqrt x=2\sqrt x\\x=8$
Plugging this into the first equation we get: $5\sqrt8-2\sqrt y=4\sqrt2\\10\sqrt2-2\sqrt y=4\sqrt2\\-2\sqrt y=-6\sqrt2\\\sqrt y=3\sqrt2\\y=18$
