$\begin{cases}\cfrac{x+y}{3} + \cfrac{2}{3} =3 \\ \cfrac{4x-y}{6 }+ \cfrac{x}{4}=1\end{cases}$
$⇔\begin{cases}\cfrac{x}{3}+\cfrac{y}{3} + \cfrac{2}{3} =3 \\ \cfrac{4x-y}{6 }+ \cfrac{x}{4}=1\end{cases}$
$⇔\begin{cases}x=\cfrac{7-y}{3} \\ \cfrac{4(7-y)-y}{6 }+ \cfrac{7-y}{4}=1\end{cases}$
$⇔\begin{cases}x=\cfrac{7-y}{3} \\ \cfrac{2[4(7-y)-y]+ 3(7-y)}{12}=1\end{cases}$
$⇔\begin{cases}x=\cfrac{7-y}{3} \\ 8(7-y)-2y+ 21-3y=12\end{cases}$
$⇔\begin{cases}x=\cfrac{7-y}{3} \\ 56-8y-2y+ 21-3y=12\end{cases}$
$⇔\begin{cases}x=\cfrac{7-y}{3} \\ 77-13y=12\end{cases}$
$⇔\begin{cases}x=\cfrac{7-y}{3} \\ 13y=65\end{cases}$
$⇔\begin{cases}x=\cfrac{7-5}{3} \\ y=5\end{cases}$
$⇔\begin{cases}x=\cfrac{2}{3} \\ y=5\end{cases}$
