\[\left\{ \begin{matrix} x^{2} + 2y = - 17 \\ y^{2} - 6x = 7\ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} (x - 3)^{2} + (y + 1)^{2} = 0\ \\ x^{2} + 2y = - 17\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[x = 3;\ \ \ y = - 1:\]
\[3^{2} + 2 \bullet ( - 1) = - 17\]
\[9 - 2 = - 17\]
\[7 \neq - 17 \Longrightarrow (3;\ - 1) \Longrightarrow\]
\[\Longrightarrow не\ решение.\]
\[Нет\ решений \Longrightarrow ч.т.д.\]