Решите систему уравнений x+y=5; x-y^2=3.

Ответ:

\[\left\{ \begin{matrix} x + y = 5\ \ \\ x - y^{2} = 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\left\{ \begin{matrix} x = 5 - y\ \ \ \ \ \ \ \ \ \ \\ 5 - y - y^{2} = 3 \\ \end{matrix} \right.\ \]

\[5 - 3 - y - y^{2} = 0\]

\[y^{2} + y - 2 = 0\]

\[y_{1} + y_{2} = - 1;\ \ \ y_{1} \cdot y_{2} = - 2\]

\[y_{1} = - 2;\ \ y_{2} = 1.\]

\[\left\{ \begin{matrix} y = - 2 \\ x = 7\ \ \ \\ \end{matrix} \right.\ \ \ \ \ или\ \ \ \ \left\{ \begin{matrix} y = 1 \\ x = 4 \\ \end{matrix} \right.\ \]

\[Ответ:(7; - 2);\ \ (4;1).\]