\(xy-3x+2y=9\)
\(\Leftrightarrow xy-3x+2y-6=3\)
\(\Leftrightarrow y\left(x+2\right)-3\left(x+2\right)=3\)
\(\Leftrightarrow\left(x+2\right)\left(y-3\right)=3\)
\(\Leftrightarrow\left\{\begin{matrix}x+2=1\\y-3=3\end{matrix}\right.\) hoặc \(\left\{\begin{matrix}x+2=-1\\y-3=-3\end{matrix}\right.\) hoặc \(\left\{\begin{matrix}x+2=3\\y-3=1\end{matrix}\right.\) hoặc \(\left\{\begin{matrix}x+2=-3\\y-3=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{\begin{matrix}x=-1\\y=6\end{matrix}\right.\) hoặc \(\left\{\begin{matrix}x=-3\\y=0\end{matrix}\right.\) hoặc \(\left\{\begin{matrix}x=1\\y=4\end{matrix}\right.\) hoặc \(\left\{\begin{matrix}x=-5\\y=2\end{matrix}\right.\)
\(x.y-3x+2y=9\Leftrightarrow x\left(y-3\right)+2y=9\)
\(\Leftrightarrow x\left(y-3\right)+2y-6=3\Leftrightarrow x\left(y-3\right)+2\left(y-3\right)=3\)
\(\Leftrightarrow\left(x+2\right)\left(y-3\right)=3\)
\(\Rightarrow x+2;y-3\in\left\{\pm1;\pm3\right\}\)
Ta có bảng sau :
| x + 2 | 1 | 3 | -1 | -3 |
| y - 3 | 3 | 1 | -3 | -1 |
| x | -1 | 1 | -3 | -5 |
| y | 6 | 4 | 0 | 2 |
Vậy x = -1 thì y = 6
x = 1 thì y = 4
x = -3 thì y = 0
x = -5 thì y = 2
