\(\Leftrightarrow2x^2+3xy+y^2+3x+2y+2=0\)
\(\Leftrightarrow2x^2+3x\left(y+1\right)+\left(y+1\right)^2+1=0\)
\(\Leftrightarrow2x^2+2x\left(y+1\right)+x\left(y+1\right)+\left(y+1\right)^2+1=0\)
\(\Leftrightarrow2x\left(x+y+1\right)+\left(y+1\right)\left(x+y+1\right)+1=0\)
\(\Leftrightarrow\left(2x+y+1\right)\left(x+y+1\right)=-1\)
TH1:
\(\left\{{}\begin{matrix}2x+y+1=-1\\x+y+1=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=-2\\y=2\end{matrix}\right.\)
TH2:
\(\left\{{}\begin{matrix}2x+y+1=1\\x+y+1=-1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=2\\y=-4\end{matrix}\right.\)
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