Решите систему уравнений: 2/x+1/(y-1)=3; 4/x+3/(y-1)=7.

\[\left\{ \begin{matrix} \frac{2}{x} + \frac{1}{y - 1} = 3\ \\ \frac{4}{x} + \frac{3}{y - 1} = 7\ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} a + b = 3\ \ \ \ \\ 2a + 3b = 7 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} a = 3 - b\ \ \ \\ 2a + 3b = 7 \\ \end{matrix} \right.\ \ \]

\[2 \bullet (3 - b) + 3b = 7\]

\[6 - 2b + 3b = 7\]

\[b = 1.\]

\[b = 1 \Longrightarrow a = 3 - 1 = 2.\]

\[\frac{2}{x} = 2\]

\[2x = 2\]

\[x = 1.\]

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

\[y - 1 = 1\]

\[y = 2.\]

\[Ответ:(1;2).\]