Solve the following systems of equations:

The given equations are:

$\frac{x}{3}+\frac{y}{4}=11 \ldots$$(i)$

$\frac{5 x}{6}-\frac{y}{3}=-7$...$(i i)$

Multiply equation $(i)$ by $\frac{1}{3}$ and equation $(i i)$ by $\frac{1}{4}$ and add both equations we get

$\frac{x}{9}+\frac{y}{12}=\frac{11}{3}$

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

$\frac{6}{3}+\frac{y}{4}=11$

$\Rightarrow \frac{y}{4}=9$

$\Rightarrow y=36$

Hence the value of $x=6$ and $y=36$.