Đáp án:
\(\left\{ \begin{array}{l}
x = \dfrac{{11}}{{40}}\\
y = - \dfrac{9}{{20}}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:y \ne \pm 2x\\
\left\{ \begin{array}{l}
\dfrac{7}{{2x + y}} + \dfrac{4}{{2x - y}} = 74\\
\dfrac{3}{{2x + y}} + \dfrac{2}{{2x - y}} = 32
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{7}{{2x + y}} + \dfrac{4}{{2x - y}} = 74\\
\dfrac{{ - 6}}{{2x + y}} - \dfrac{4}{{2x - y}} = - 64
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{1}{{2x + y}} = 10\\
\dfrac{3}{{2x + y}} + \dfrac{2}{{2x - y}} = 32
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{2}{{2x - y}} = 2\\
\dfrac{1}{{2x + y}} = 10
\end{array} \right.\\
\to \left\{ \begin{array}{l}
2x - y = 1\\
2x + y = \dfrac{1}{{10}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
4x = \dfrac{{11}}{{10}}\\
y = 2x - 1
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{11}}{{40}}\\
y = - \dfrac{9}{{20}}
\end{array} \right.
\end{array}\)
