Solve the following systems of equations:

The given equations are:

$x+\frac{y}{2}=4 \ldots$$\ldots(i)$

$\frac{x}{3}+2 y=5$$. .($ ii $)$

Multiply equation $(i)$ by 4 and subtract equations $(i)-(i i)$, we get

$4 x+2 y=16$

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

$3+\frac{y}{2}=4$

$\Rightarrow \frac{y}{2}=1$

$\Rightarrow y=2$

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