Đáp án:
\(\left\{ \begin{array}{l}
x = \dfrac{{10397}}{{109142}}\\
y = \dfrac{{9028}}{{54571}}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne \left\{ { - \dfrac{y}{3};\dfrac{{3y}}{2}} \right\}\\
\left\{ \begin{array}{l}
\dfrac{4}{{2x - 3y}} + \dfrac{5}{{3x + y}} = - 2\\
- \dfrac{5}{{2x - 3y}} + \dfrac{3}{{3x + y}} = 21
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{20}}{{2x - 3y}} + \dfrac{{25}}{{3x + y}} = - 2\\
- \dfrac{{20}}{{2x - 3y}} + \dfrac{{12}}{{3x + y}} = 84
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{25}}{{3x + y}} + \dfrac{{12}}{{3x + y}} = 82\\
\dfrac{4}{{2x - 3y}} + \dfrac{5}{{3x + y}} = - 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{37}}{{3x + y}} = 82\\
\dfrac{4}{{2x - 3y}} + \dfrac{5}{{3x + y}} = - 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
3x + y = \dfrac{{37}}{{82}}\\
\dfrac{4}{{2x - 3y}} + 5:\dfrac{{37}}{{82}} = - 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
3x + y = \dfrac{{37}}{{82}}\\
\dfrac{4}{{2x - 3y}} = - \dfrac{{484}}{{37}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
3x + y = \dfrac{{37}}{{82}}\\
2x - 3y = - \dfrac{{37}}{{121}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{37}}{{82}} - 3x\\
2x - 3\left( {\dfrac{{37}}{{82}} - 3x} \right) = - \dfrac{{37}}{{121}}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
11x = \dfrac{{10397}}{{9922}}\\
y = \dfrac{{37}}{{82}} - 3x
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{{10397}}{{109142}}\\
y = \dfrac{{9028}}{{54571}}
\end{array} \right.
\end{array}\)
