PL.SOLVE SQRT X+Y=11 & X+SQRT Y=7

From the equations it can be inferred that y>=0 and x+y>=0(In the first equation I am not sure whether the root is for x+y or for only x.)

So, I will just give the idea. Bring all non squareroot terms one side, the other terms other side in both the equations and square on both sides. Now you have two quadratic eqns in x&y which can be easily solved.