\(\Leftrightarrow5y-3x-2xy+11=0\)
\(\Leftrightarrow x\left(-3-2y\right)=-5y-11\)
\(\Rightarrow x=\dfrac{-5y-11}{-2y-3}\)
Để x nguyên thì \(-5y-11⋮-2y-3\)
\(\Rightarrow5y+7,5+3,5⋮2y+3\)
\(\Rightarrow7⋮2y+3\)\(\Rightarrow2y+3\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)
\(\Rightarrow y\in\left\{-5;-2;-1;2\right\}\)
\(\Rightarrow x\in\left\{2;-1;6;3\right\}\)
Vậy pt có nghiệm là (2;-5);(-1;-2);(6;-1);(3;2).
\(5y-3x=2xy-11\)
\(\Rightarrow2xy+3x-5y-11=0\)
\(\Rightarrow4xy+6x-10y-22=0\)
\(\Rightarrow\left(4xy+6x\right)-\left(10y+15\right)=7\)
\(\Rightarrow2x\left(2y+3\right)-5\left(2y+3\right)=7\)
\(\Rightarrow\left(2x-5\right)\left(2y+3\right)=7\)
Ta có các TH sau:
TH1: \(\left\{\begin{matrix}2x-5=1\\2y+3=7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=3\\y=2\end{matrix}\right.\)
TH2: \(\left\{\begin{matrix}2x-5=-1\\2y+3=-7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=2\\y=-5\end{matrix}\right.\)
TH3: \(\left\{\begin{matrix}2x-5=7\\2y+3=1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=6\\y=-1\end{matrix}\right.\)
TH4: \(\left\{\begin{matrix}2x-5=-7\\2y+3=-1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=-1\\y=-2\end{matrix}\right.\)
