Đáp án:
`y=-2` và `x=5`
Giải thích các bước giải:
\(\begin{array}{l}
\text{Điều kiện: }x \ne 2y;x \ne \dfrac{y}{2}\\
\left\{ \begin{array}{l}
\dfrac{{3 - (- 1)}}{{x - 2y}} = \dfrac{1}{2} - \dfrac{1}{{18}}\\
\dfrac{2}{{2x - y}} + \dfrac{3}{{x - 2y}} = \dfrac{1}{2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{4}{{x - 2y}} = \dfrac{4}{9}\\
\dfrac{2}{{2x - y}} + \dfrac{3}{{x - 2y}} = \dfrac{1}{2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x - 2y = 9\\
\dfrac{2}{{2x - y}} + \dfrac{3}{{x - 2y}} = \dfrac{1}{2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 2y + 9\\
\dfrac{2}{{2\left( {2y + 9} \right) - y}} + \dfrac{3}{{2y + 9 - 2y}} = \dfrac{1}{2}\left( 1 \right)
\end{array} \right.\\
\left( 1 \right) \to \dfrac{2}{{3y + 18}} + \dfrac{1}{3} = \dfrac{1}{2}\\
\to \dfrac{2}{{3y + 18}} = \dfrac{1}{6}\\
\to 3y + 18 = 12\\
\to 3y = - 6\\
\to y = - 2\\
\to x = 5
\end{array}\)
