Solve the following systems of equations:

The given equations are:

$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$

$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

Multiply equation $(i)$ by 3 and add both equations we get

$\frac{6}{\sqrt{x}}+\frac{9}{\sqrt{y}}=6$

Put the value of $x$ in equation $(i)$, we get

$\frac{2}{\sqrt{4}}+\frac{3}{\sqrt{y}}=2$

$\Rightarrow \sqrt{y}=3$

$\Rightarrow y=9$

Hence the value of $x=4$ and $y=9$