Solve the following systems of equations:

The given equations are:

$\frac{15}{u}+\frac{2}{v}=17$

$\frac{1}{u}+\frac{1}{v}=\frac{36}{5} \ldots(i i)$

Multiply equation (ii) by 2 and subtract (ii) from (i), we get

$\frac{15}{u}+\frac{2}{v}=17$

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

$\frac{15}{5}+\frac{2}{v}=17$

$\Rightarrow \frac{2}{v}=14$

$\Rightarrow v=\frac{1}{7}$

Hence the value of $u=5$ and $v=\frac{1}{7}$.