\(x+2y+xy=2\)
\(\Rightarrow x\left(1+y\right)+2y+2-2=2\)
\(\Rightarrow x\left(1+y\right)+2\left(y+1\right)=4\)
\(\Rightarrow\left(y+1\right)\left(x+2\right)=4\)
\(\Rightarrow\left(x+2\right);\left(y+1\right)\in\left\{-1;1;-2;2;-4;4\right\}\)
\(\Rightarrow\left(x;y\right)\in\left\{\left(-3;-5\right);\left(-1;3\right);\left(-4;-3\right);\left(0;1\right);\left(-6;-2\right);\left(2;0\right)\right\}\)
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