Решите систему уравнений: 2/x+3/(y-2)=5; 5/x-4/(y-2)=1.

\[\left\{ \begin{matrix} \frac{2}{x} + \frac{3}{y - 2} = 5\ \\ \frac{5}{x} - \frac{4}{y - 2} = 1\ \\ \end{matrix} \right.\ \]

\[5 \bullet (2,5 - 1,5b) - 4b = 1\]

\[12,5 - 7,5b - 4b = 1\]

\[- 11,5b = - 11,5\]

\[b = 1 \Longrightarrow a = 2,5 - 1,5 \bullet 1 =\]

\[= 2,5 - 1,5 = 1.\]

\[\frac{1}{x} = 1 \Longrightarrow x = 1.\]

\[\frac{1}{y - 2} = 1\]

\[y - 2 = 1 \Longrightarrow y = 3.\]

\[Ответ:(1;3).\]