Find the value of x and y for the following two equations:
$$ \sqrt{x} + y = 7 $$ $$ x + \sqrt{y} = 11 $$
My solutuin is based on a guess. From the above, the instinct is that both x and y are the numbers like 1, 4, 9, 16, etc. If we rewrite the equations as follows:
$$ x = (7 - y)^2 $$ $$ y = (11 -x)^2 $$
The hunch is y is less than 7 and x less than 11.
So x = 9 and y = 4. Both are exactly the solutions.