Đáp án:
\[\left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = 5\\
y = 9
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 9\\
y = 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 3\\
y = - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x = - 1\\
y = 3
\end{array} \right.
\end{array} \right.\]
Giải thích các bước giải:
Ta có:
\[\begin{array}{l}
4\left( {x + y} \right) = 11 + xy\\
\Leftrightarrow xy - 4x - 4y + 11 = 0\\
\Leftrightarrow x\left( {y - 4} \right) - 4\left( {y - 4} \right) = 5\\
\Leftrightarrow \left( {x - 4} \right)\left( {y - 4} \right) = 5\\
\Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - 4 = 1\\
y - 4 = 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 4 = 5\\
y - 4 = 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 4 = - 1\\
y - 4 = - 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x - 4 = - 5\\
y - 4 = - 1
\end{array} \right.
\end{array} \right. \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = 5\\
y = 9
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 9\\
y = 5
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 3\\
y = - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x = - 1\\
y = 3
\end{array} \right.
\end{array} \right.
\end{array}\]
