\(\Leftrightarrow x^2-xy-5x+4y+9=0\)
\(\Leftrightarrow\left(x^2-xy\right)-\left(4x-4y\right)-x+9=0\)
\(\Leftrightarrow x\left(x-y\right)-4\left(x-y\right)-x+9=0\)
\(\Leftrightarrow\left(x-y\right)\left(x-4\right)-\left(x-4\right)+5=0\)
\(\Leftrightarrow\left(x-4\right)\left(x-y-1\right)=-5\)
Do \(x;y\in Z\Rightarrow\left(x-4\right);\left(x-y-1\right)\in Z\)
Ta có các trường hợp sau
+ TH1:
\(\left\{{}\begin{matrix}x-4=1\\x-y-1=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=9\end{matrix}\right.\)
+ TH2:
\(\left\{{}\begin{matrix}x-4=-1\\x-y-1=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-3\end{matrix}\right.\)
+ TH3:
\(\left\{{}\begin{matrix}x-4=5\\x-y-1=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=9\\y=9\end{matrix}\right.\)
+ TH4:
\(\left\{{}\begin{matrix}x-4=-5\\x-y-1=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=-3\end{matrix}\right.\)