Answer
$x=4,y=25$
Work Step by Step
Our constraints are: $x,y\geq0$. Then if we add the first and second equations we get: $8\sqrt x=16\\\sqrt x=2\\x=4$
Plugging this into the first equation we get: $3\sqrt4+5\sqrt y=31\\3\cdot2+5\sqrt y=31\\5\sqrt y=25\\\sqrt y=5\\y=25$
