Đáp án:
\[\left( {x;y} \right) = \left\{ {\left( {8;2} \right);\left( {6; - 8} \right);\left( {12; - 2} \right);\left( {2; - 4} \right)} \right\}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
xy + 3x - 7y = 26\\
\Leftrightarrow \left( {xy + 3x} \right) - \left( {7y + 21} \right) = 26 - 21\\
\Leftrightarrow x\left( {y + 3} \right) - 7\left( {y + 3} \right) = 5\\
\Leftrightarrow \left( {x - 7} \right)\left( {y + 3} \right) = 5\\
5 = 1.5 = \left( { - 1} \right).\left( { - 5} \right)\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 7 = 1\\
y + 3 = 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 7 = - 1\\
y + 3 = - 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 7 = 5\\
y + 3 = 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 7 = - 5\\
y + 3 = - 1
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = 8\\
y = 2
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 6\\
y = - 8
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 12\\
y = - 2
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 2\\
y = - 4
\end{array} \right.
\end{array} \right.\\
\Rightarrow \left( {x;y} \right) = \left\{ {\left( {8;2} \right);\left( {6; - 8} \right);\left( {12; - 2} \right);\left( {2; - 4} \right)} \right\}
\end{array}\)
