Solve the following systems of equations:

The given equations are:

$\frac{1}{7 x}+\frac{1}{6 y}=3$$\cdots(i)$

$\frac{1}{2 x}-\frac{1}{3 y}=5$...(ii)

Multiply equation (ii) by $\frac{1}{2}$ and add both equations we get

$\frac{1}{7 x}+\frac{1}{6 y}=3$

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

$\frac{1}{7 \times \frac{1}{14}}+\frac{1}{6 y}=3$

$\Rightarrow \frac{1}{6 y}=1$

$\Rightarrow y=\frac{1}{6}$

Hence the value of $x=\frac{1}{14}$ and $y=\frac{1}{6}$