\[\left\{ \begin{matrix} y = x + 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + y^{2} + 4x + 4y = - 1 \\ \end{matrix} \right.\ \]
\[2x^{2} + 16x + 33 = 0\]
\[D = 16^{2} - 4 \cdot 2 \cdot 33 =\]
\[= 256 - 264 = - 8 < 0 \Longrightarrow\]
\[\Longrightarrow нет\ решения.\]
\[\Longrightarrow ч.т.д.\]