Solve the following systems of equations:

The given equations are:

$\frac{x y}{x+y}=\frac{6}{5}$

$6 x+6 y=5 x y \quad \ldots(i)$

$\frac{x y}{y-x}=6$

$6 y-6 x=x y \quad \ldots(i i)$

Add both equations, we get

$6 x+6 y=5 x y$

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

$22 \times-\frac{1}{11}+15 v=5$

$\Rightarrow 15 v=3$

$\Rightarrow v=\frac{1}{5}$

Hence the value of $x=2$ and $y=3$