Đáp án:
\[\left[ \begin{array}{l}
\left\{ \begin{array}{l}
y = 0\\
x = 13
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 1\\
y = 3
\end{array} \right.
\end{array} \right.\]
Giải thích các bước giải:
Ta có:
\[\begin{array}{l}
2xy + x + 2y = 13\\
\Leftrightarrow \left( {2xy + x} \right) + \left( {2y + 1} \right) = 14\\
\Leftrightarrow x\left( {2y + 1} \right) + \left( {2y + 1} \right) = 14\\
\Leftrightarrow \left( {2y + 1} \right)\left( {x + 1} \right) = 14\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
2y + 1 = 1\\
x + 1 = 14
\end{array} \right.\\
\left\{ \begin{array}{l}
2y + 1 = 14\\
x + 1 = 1
\end{array} \right.\\
\left\{ \begin{array}{l}
2y + 1 = 2\\
x + 1 = 7
\end{array} \right.\\
\left\{ \begin{array}{l}
2y + 1 = 7\\
x + 1 = 2
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
y = 0\\
x = 13
\end{array} \right.\left( {t/m} \right)\\
\left\{ \begin{array}{l}
y = \frac{{13}}{2}\\
x = 0
\end{array} \right.\left( L \right)\\
\left\{ \begin{array}{l}
y = \frac{1}{2}\\
x = 6
\end{array} \right.\left( L \right)\\
\left\{ \begin{array}{l}
y = 3\\
x = 1
\end{array} \right.\left( {t/m} \right)
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
y = 0\\
x = 13
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 1\\
y = 3
\end{array} \right.
\end{array} \right.
\end{array}\]
