Solve the following systems of equations:

The given equations are:

$\frac{2}{x}+\frac{3}{y}=13$..(i)

$\frac{5}{x}-\frac{4}{y}=-2 \ldots(i i)$

Multiply equation (i) by 4 and equation (ii) by 3 and add both equations we get

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

$\frac{2}{\frac{1}{2}}+\frac{3}{y}=13$

$\Rightarrow \frac{3}{y}=9$

$\Rightarrow y=\frac{1}{3}$

Hence the value of $x=\frac{1}{2}$ and $y=\frac{1}{3}$.