$\begin{cases}(3x-1)(2y+1)=(x+1)(6y+1)\\(x+2)(4y-1)=(2x+2)(2y+2)\end{cases}$
$↔\begin{cases}6xy+3x-2y-1=6xy+x+6y+1\\4xy-x+8y-2=4xy+4x+4y+4\end{cases}$
$↔\begin{cases}2x-8y-2=0\\-5x+4y-6=0\end{cases}$
$↔\begin{cases}x=4y+1\\-5(4y+1)+4y-6=0\end{cases}$
$↔\begin{cases}x=4y+1\\-20y-5+4y-6=0\end{cases}$
$↔\begin{cases}x=4y+1\\-16y-11=0\end{cases}$
$↔\begin{cases}x=4.\cfrac{-11}{16}+1\\y=\cfrac{-11}{16}\end{cases}$
$↔\begin{cases}x=\cfrac{-7}{4}\\y=\cfrac{-11}{16}\end{cases}$
