Two reals \(x\text{, }y\) satisfy below two equations:

\[\frac{xy-(x+y)+1}{x^2+y^2-2(x+y)+2}=-\frac{1}{2}\]

\[\sqrt{\pi}x-2y=\sqrt{11}+\sqrt{13}+\sqrt{19}+\sqrt{97}\]

Find the value of \(x+y\).

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