Please reason step by step, and put your final answer within \boxed{}.
If $x$ and $y$ are real numbers and satisfy $|9y+1-x|=\sqrt{x-4}⋅\sqrt{4-x}$, find the value of $2x\sqrt{\frac{1}{x}}+\sqrt{9y}-\frac{{\sqrt{x}}}{2}+y\sqrt{\frac{1}{y}}$.
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