Ta có : \(xy+3x-7y=21\)
\(\Leftrightarrow xy+3x-7y-21=0\)
\(\Leftrightarrow x\left(y+3\right)-7\left(y+3\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(y+3\right)=0\)
\(\Rightarrow x-7=0\)
\(\Leftrightarrow x=0+7\)
\(\Leftrightarrow x=7\)
\(\Rightarrow y+3=0\)
\(\Leftrightarrow y=0-3\)
\(\Leftrightarrow y=-3\)
\(\text{Vậy }\orbr{\begin{cases}x=7;y\inℤ\\x\inℤ;y=-3\end{cases}}\)