Решите систему уравнений способом сложения 3x+y=7; 2x^2-y=7.

Ответ:

\[\left\{ \begin{matrix} 3x + y = 7\ \ \\ 2x^{2} - y = 7 \\ \end{matrix} \right.\ \ ( + )\text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} 3x + 2x^{2} = 14 \\ y = 7 - 3x\ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} 2x^{2} + 3x - 14 = 0 \\ y = 7 - 3x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[2x^{2} + 3x - 14 = 0\]

\[D = 9 + 112 = 121\]

\[x_{1} = \frac{- 3 + 11}{4} = 2;\ \ y_{1} = 7 - 3 \cdot 2 = 1\ \]

\[x_{2} = \frac{- 3 - 11}{4} = - \frac{14}{4} = - 3,5;\]

\[y_{2} = 7 - 3 \cdot ( - 3,5) = 7 + 10,5 = 17,5.\]

\[\left\{ \begin{matrix} x = 2 \\ y = 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = - 3,5\ \ \\ y = 17,5\ \ \ \\ \end{matrix} \right.\ \ \]

\[Ответ:(2;1);( - 3,5;\ 17,5).\]