Решите систему уравнений способом подстановки: 2x+y=3; 3x^2+4xy+7y^2+x+8y=5.

Ответ:

\[\left\{ \begin{matrix} 2x + y = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x^{2} + 4xy + 7y^{2} + x + 8y = 5 \\ \end{matrix} \right.\ \]

\[23x^{2} - 87x + 82 = 0\]

\[D = 7569 - 7544 = 25\]

\[x_{1} = \frac{(87 + 5)}{46} = \frac{92}{46} = 2;\]

\[x_{2} = \frac{(87 - 5)}{46} = \frac{82}{46} = \frac{41}{23}.\]

\[y_{1} = 3 - 2 \cdot 2 = - 1;\]

\[y_{2} = 3 - 2 \cdot \frac{41}{23} = 3 - \frac{82}{23} =\]

\[= 3 - 3\frac{13}{23} = - \frac{13}{23}.\]

\[Ответ:(2; - 1);\left( \frac{41}{23}; - \frac{13}{23} \right).\]