Question

$\sqrt{x} +y=11 and x+ \sqrt{y} =9,find the value of x and y.$

Answer 1

From equation 1:
$y = 11 - \sqrt{x}$
Put this in the second equation:
$x + \sqrt{11- \sqrt{x} } = 9 \\ \sqrt{11- \sqrt{x} } = 9-x \\ 11- \sqrt{x} = 81 + x^{2} -18x \\ x^{2} -18x+70=- \sqrt{x} \\ ( x^{2} -18x+70)^2 = x$

If the above equation is solved, it will give x = 
12.818413439584889044550365692233
11.751712718159879743198001332962 
6.0786105775653921897299216578218 
5.3512632646898390225217113169828

and then y can be found out very easily