\[y = 3x + 1\ \ \ \ \ \ и\ \ \ y = \frac{x + 27}{x - 3}\]
\[3x + 1 = \frac{x + 27}{x - 3}\]
\[ОДЗ:\ \ x \neq 3\]
\[(3x + 1)(x - 3) = x + 27\]
\[3x^{2} - 9x + x - 3 - x - 27 = 0\]
\[3x² - 9x - 30 = 0\ \ \ \ \ |\ :3\]
\[x^{2} - 3x - 10 = 0\]
\[x_{1} + x_{2} = 3\]
\[x_{1} \cdot x_{2} = - 10 \Longrightarrow\]
\[x_{1} = 5 \Longrightarrow y_{1} = 3 \cdot 5 + 1 = 16\]
\[x_{2} = - 2 \Longrightarrow y_{2} = 3 \cdot ( - 2) + 1 =\]
\[= - 5\]
\[Ответ:\ \ (5;16);\ \ \ ( - 2; - 5).\]