Найдите координаты точек пересечения графиков функций: y=3x+1 и y=(x+27)/(x-3).

Ответ:

\[y = 3x + 1\ \ \ \ \ \ и\ \ \ y = \frac{x + 27}{x - 3}\]

\[3x + 1 = \frac{x + 27}{x - 3}\]

\[ОДЗ:\ \ x \neq 3\]

\[(3x + 1)(x - 3) = x + 27\]

\[3x^{2} - 9x + x - 3 - x - 27 = 0\]

\[3x² - 9x - 30 = 0\ \ \ \ \ |\ :3\]

\[x^{2} - 3x - 10 = 0\]

\[x_{1} + x_{2} = 3\]

\[x_{1} \cdot x_{2} = - 10 \Longrightarrow\]

\[x_{1} = 5 \Longrightarrow y_{1} = 3 \cdot 5 + 1 = 16\]

\[x_{2} = - 2 \Longrightarrow y_{2} = 3 \cdot ( - 2) + 1 =\]

\[= - 5\]

\[Ответ:\ \ (5;16);\ \ \ ( - 2; - 5).\]