a) \(xy-2x-3y+6=0\)
\(\Leftrightarrow xy-2x-3y+3.2=0\)
\(\Leftrightarrow x\left(y-2\right)-3\left(y-2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(y-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\y-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0+3\\y=0+2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\y=2\end{matrix}\right.\)