Solve the following systems of equations:

The given equations are:

$\frac{4}{x}+5 y=7 \ldots(i)$

$\frac{3}{x}+4 y=5$ ...(ii)

Multiply equation $(i)$ by 4 and equation $(i i)$ by 5 and subtract (ii) from (i) we get

$\frac{16}{x}+20 y=28$

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

$\frac{4}{\frac{1}{3}}+5 y=7$

$\Rightarrow 5 y=-5$

$\Rightarrow y=-1$

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