solve the equations simuntaneousely  X +square root of y=11  square root of x+y=7
From the bottom equation:
Inserting this into the top equation:
<-- Square both sides
Since the solution is going to turn out to be ugly anyway, I'm going to use a trick. (They use it in the referred thread as well.)
Using the rational root theorem, you can find one nice solution: x = 9. You can get the rest numerically: x = 7.86869, 12.8481, 14.2832.