Find the value of X and Y from the given equation : sqrt(X)+Y=7 & sqrt(Y)+X=11

Usually these types of problems can be very challenging. But no need to do any "real" work for this problem since the numbers a so easy to work with. Clearly x and y have to be 9 and 4 (why?) So we'll just check them...
3+4=7 so far so good...
2+9=11...perfect
x=9, y=4