Solve the following systems of equations:

The given equations are:

$\frac{1}{2 x}+\frac{1}{3 y}=2...(i)

$\frac{1}{3 x}+\frac{1}{2 y}=\frac{13}{6}$..$(i i)$

Multiply equation $(i)$ by $\frac{1}{2}$ and $(i i)$ by $\frac{1}{3}$ and subtract equation (ii) from (i) we get

$\frac{1}{4 x}+\frac{1}{6 y}=1$

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

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

$\frac{1}{3 y}=2-1$

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

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

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