5y−3x=2xy−11
\Rightarrow2xy+3x-5y-11=0⇒2xy+3x−5y−11=0
\Rightarrow4xy+6x-10y-22=0⇒4xy+6x−10y−22=0
\Rightarrow\left(4xy+6x\right)-\left(10y+15\right)=7⇒(4xy+6x)−(10y+15)=7
\Rightarrow2x\left(2y+3\right)-5\left(2y+3\right)=7⇒2x(2y+3)−5(2y+3)=7
\Rightarrow\left(2x-5\right)\left(2y+3\right)=7⇒(2x−5)(2y+3)=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.{2x−5=12y+3=7⇒{x=3y=2
TH2: \left\{\begin{matrix}2x-5=-1\\2y+3=-7\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=2\\y=-5\end{matrix}\right.{2x−5=−12y+3=−7⇒{x=2y=−5
TH3: \left\{\begin{matrix}2x-5=7\\2y+3=1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=6\\y=-1\end{matrix}\right.{2x−5=72y+3=1⇒{x=6y=−1
TH4: \left\{\begin{matrix}2x-5=-7\\2y+3=-1\end{matrix}\right.\Rightarrow\left\{\begin{matrix}x=-1\\y=-2\end{matrix}\right.{2x−5=−72y+3=−1⇒{x=−1y=−2
Vậy......................................