\[\left\{ \begin{matrix} x^{2} - 10y = 23\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} - 2x + 1 + y^{2} - 10y + 25 = 0 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x^{2} - 10y = 23\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x - 1)^{2} + (y - 5)^{2} = 0 \\ \end{matrix} \right.\ \]
\[1^{2} - 10 \cdot 5 = 23\]
\[1 - 50 = 23\]
\[- 49 \neq 23 \Longrightarrow (1;5) -\]
\[не\ решение.\]
\[Нет\ решений \Longrightarrow ч.т.д.\]