\[\left\{ \begin{matrix} y = x + 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + y^{2} + 2x + 4y = - 1 \\ \end{matrix} \right.\ \]
\[2x^{2} + 12x + 22 = 0\ \ \ \ \ \ \ \ |\ :2\]
\[x^{2} + 6x + 11 = 0\]
\[D = 6^{2} - 4 \cdot 1 \cdot 11 = 36 - 44 =\]
\[= - 8 < 0 - \Longrightarrow нет\ решения.\]
\[\Longrightarrow ч.т.д.\]