\(xy-2x+3y=9\)
\(\Leftrightarrow xy-2x+3y-6=9-6\)
\(\Leftrightarrow x\left(y-2\right)+3\left(y-2\right)=3\)
\(\Leftrightarrow\left(y-2\right)\left(x+3\right)=3\)
Vì \(x,y\in Z\Leftrightarrow y-2;x+3\in Z,y-2;x+3\inƯ\left(3\right)\)
Ta có bảng :
\(y\) | \(y-2\) | \(x+3\) | \(x\) | \(Đk\) \(x;y\in Z\) |
\(3\) | \(1\) | \(3\) | \(0\) | tm |
\(5\) | \(3\) | \(1\) | \(-2\) | tm |
\(1\) | \(-1\) | \(-3\) | \(-6\) | tm |
\(-1\) | \(-3\) | \(-1\) | \(-4\) | tm |
Vậy ...