Đáp án:
\(\left( {3;4} \right);\,\,\left( {1; - 10} \right);\,\,\left( {9; - 2} \right);\,\,\left( { - 5; - 4} \right)\)
Giải thích các bước giải:
\(\begin{array}{l}
xy - 2y + 3x - 6 = 7\\
\Leftrightarrow y\left( {x - 2} \right) + 3\left( {x - 2} \right) = 7\\
\Leftrightarrow \left( {x - 2} \right)\left( {y + 3} \right) = 7\\
\Rightarrow x - 2 \in U\left( 7 \right) = \left\{ { \pm 1; \pm 7} \right\}\\
TH1:\,\,\left\{ \begin{array}{l}
x - 2 = 1\\
y + 3 = 7
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 3\\
y = 4
\end{array} \right.\,\,\left( {tm} \right)\\
TH2:\,\,\left\{ \begin{array}{l}
x - 2 = - 1\\
y + 3 = - 7
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 1\\
y = - 10
\end{array} \right.\,\,\left( {tm} \right)\\
TH3:\,\,\left\{ \begin{array}{l}
x - 2 = 7\\
y + 3 = 1
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 9\\
y = - 2
\end{array} \right.\,\,\left( {tm} \right)\\
TH4:\,\,\left\{ \begin{array}{l}
x - 2 = - 7\\
y + 3 = - 1
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - 5\\
y = - 4
\end{array} \right.\,\,\left( {tm} \right)\\
Vay\,\,cac\,\,nghiem\,\,nguyen\,\,cua\,\,pt\,\,la:\\
\left( {3;4} \right);\,\,\left( {1; - 10} \right);\,\,\left( {9; - 2} \right);\,\,\left( { - 5; - 4} \right)
\end{array}\)
