Решите систему уравнений способом сложения 4x-y=9; 3x^2+y=11.

Ответ:

\[\left\{ \begin{matrix} 4x - y = 9\ \ \ \ \\ 3x^{2} + y = 11 \\ \end{matrix} \right.\ ( + )\]

\[\left\{ \begin{matrix} 4x + 3x^{2} = 20 \\ y = 4x - 9\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[3x^{2} + 4x - 20 = 0\]

\[D = 4 + 60 = 64\]

\[x_{1} = \frac{- 2 + 8}{3} = \frac{6}{3} = 2;\]

\[y_{1} = 4 \cdot 2 - 9 = - 5;\]

\[x_{2} = \frac{- 2 - 8}{3} = - \frac{10}{3};\]

\[y_{2} = 4x - 9 = 4 \cdot \left( - \frac{10}{3} \right) - 9 =\]

\[= - \frac{40}{3} - 9 = - \frac{67}{3}\]

\[\left\{ \begin{matrix} x = 2\ \ \ \\ y = - 5 \\ \end{matrix} \right.\ \ \ \ \ и\ \ \ \ \left\{ \begin{matrix} x = - \frac{10}{3}\ \\ y = - \frac{67}{3}\ \\ \end{matrix} \right.\ \]

\[Ответ:(2;\ - 5);\left( - \frac{10}{3}; - \frac{67}{3} \right).\]