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2015-06-20T22:43:57+05:30

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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
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