Solve the following simultaneous Linear Expression

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$$\begin{gathered} \frac{1}{x}+\frac{1}{y}=\frac{1}{xy} \\ \frac{x+y}{xy}=\frac{1}{xy} \\ x+y=1 ... \left(i\right) \\ Also, \sqrt{\frac{x}{y}}=4 \\ Squarring both the sides: \\ \frac{x}{y}=16 \\ x=16y \\ Putting this value in \left(i\right) \\ 16y+y=1 \\ 17y=1 \\ y=\frac{1}{17} \\ Putting this value in \left(i\right) \\ x+\frac{1}{17}=1 \\ x=1-\frac{1}{17} \\ x=\frac{16}{17} \\ Hence x=\frac{16}{17}, y=\frac{1}{17} \end{gathered}$$

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