Đáp án:
\[\left\{ \begin{array}{l}
x = \frac{{121}}{{61}}\\
y = - \frac{{146}}{{21}}
\end{array} \right.\]
Giải thích các bước giải:
ĐKXĐ: \(\left\{ \begin{array}{l}
x \ne 2\\
y \ne - 7
\end{array} \right.\)
Ta có:
\(\begin{array}{l}
\left\{ \begin{array}{l}
\frac{{5x - 9}}{{x - 2}} + \frac{{4y + 31}}{{y + 7}} = 11\\
\frac{{3x - 4}}{{x - 2}} + \frac{{2y + 19}}{{y + 7}} = - 11
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{{5\left( {x - 2} \right) + 1}}{{x - 2}} + \frac{{4\left( {y + 7} \right) + 3}}{{y + 7}} = 11\\
\frac{{3\left( {x - 2} \right) + 2}}{{x - 2}} + \frac{{2\left( {y + 7} \right) + 5}}{{y + 7}} = - 11
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
5 + \frac{1}{{x - 2}} + 4 + \frac{3}{{y + 7}} = 11\\
4 + \frac{2}{{x - 2}} + 2 + \frac{5}{{y + 7}} = - 11
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{1}{{x - 2}} + \frac{3}{{y + 7}} = 2\\
\frac{2}{{x - 2}} + \frac{5}{{y + 7}} = - 17
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\frac{1}{{x - 2}} = - 61\\
\frac{1}{{y + 7}} = 21
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x - 2 = - \frac{1}{{61}}\\
y + 7 = \frac{1}{{21}}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = \frac{{121}}{{61}}\\
y = - \frac{{146}}{{21}}
\end{array} \right.
\end{array}\)
