Đáp án:
\[\left\{ \begin{array}{l}
x = 9\\
y = 1
\end{array} \right.\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\left\{ \begin{array}{l}
4\left( {x + y} \right) = 5\left( {x - y} \right)\\
\frac{{40}}{{x + y}} + \frac{{40}}{{\left( {x - y} \right)}} = 9
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x + y = \frac{5}{4}\left( {x - y} \right)\\
\frac{{40}}{{x + y}} + \frac{{40}}{{x - y}} = 9
\end{array} \right.\\
\Rightarrow \frac{{40}}{{\frac{5}{4}\left( {x - y} \right)}} + \frac{{40}}{{x - y}} = 9\\
\Leftrightarrow \frac{{160}}{{5\left( {x - y} \right)}} + \frac{{40}}{{x - y}} = 9\\
\Leftrightarrow \frac{{72}}{{\left( {x - y} \right)}} = 9 \Leftrightarrow x - y = 8 \Rightarrow x + y = 10\\
\Rightarrow \left\{ \begin{array}{l}
x - y = 8\\
x + y = 10
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 9\\
y = 1
\end{array} \right.
\end{array}\)
