\[\boxed{\text{1109.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\textbf{а)}\ y = x + 1;\ \ y = \frac{2}{x}\]
\[x + 1 = \frac{2}{x}\ \ \ \ \ \ \ | \cdot x \neq 0\]
\[x^{2} + x - 2 = 0\]
\[x_{1} + x_{2} = - 1;\ \ x_{1} \cdot x_{2} = - 2\]
\[x_{1} = - 2;\ \ \ x_{2} = 1.\]
\[y_{1} = - 1;\ \ \ y_{2} = 2.\]
\[Ответ:пересекаются;\ \ \]
\[точки\ пересечения\ \]
\[( - 2; - 1);(1;2).\]
\[\textbf{б)}\ \ y = - 2x - 2;\ \ y = \frac{1}{x}\]
\[- 2x - 2 = \frac{1}{x}\ \ \ \ | \cdot x \neq 0\]
\[- 2x^{2} - 2x - 1 = 0\]
\[2x^{2} + 2x + 1 = 0\]
\[D_{1} = 1 - 2 = - 1 < 0\]
\[нет\ корней.\]
\[Ответ:не\ пересекаются.\]