Solve the following systems of equations:

The given equations are:

$2(3 u-v)=5 u v$

$6 u-2 v=5 u v$$\ldots(i)$

$2(u+3 v)=5 u v$

$2 u+6 v=5 u v$$\ldots(i i)$

Multiply equation ( $i$ ) by 3 and add both equations, we get

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

$6 u-2 \times 1=5 u \times 1$

$\Rightarrow u=2$

Hence the value of $u=2$ and $v=1$.