Решите систему уравнений: x^2+y^2=25; x+y=7.

\[\left\{ \begin{matrix} x² + y^{2} = 25\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x + y = 7 \Longrightarrow y = 7 - x \\ \end{matrix} \right.\ \]

\[x^{2} + (7 - x)^{2} = 25\]

\[x^{2} + 49 - 14x + x^{2} = 25\]

\[2x² - 14x + 24 = 0\ \ \ \ |\ :2\]

\[x^{2} - 7x + 12 = 0\]

\[D = 49 - 48 = 1\]

\[x_{1} = \frac{7 + 1}{2} = 4;\ \ \ \ \ \ \ \]

\[x_{2} = \frac{7 - 1}{2} = 3\]

\[y_{1} = 7 - 4 = 3;\ \ \ \ \ \ \ \]

\[y_{2} = 7 - 3 = 4\]

\[Ответ:(4;3);\ \ (3;4).\]