Решите систему уравнений: 4x^2+y^2=29; 2x-y=7.

\[\left\{ \begin{matrix} 4x² + y² = 29\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x - y = 7 \Longrightarrow y = 2x - 7 \\ \end{matrix} \right.\ \]

\[4x^{2} + (2x - 7)^{2} = 29\]

\[4x^{2} + 4x^{2} - 28x + 49 = 29\]

\[8x² - 28x + 20 = 0\ \ \ \ \ |\ :4\]

\[2x^{2} - 7x + 5 = 0\]

\[D = 49 - 40 = 9\]

\[x_{1} = \frac{7 + 3}{4} = \frac{10}{4} = 2,5;\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \]

\[\text{\ \ \ \ }x_{2} = \frac{7 - 3}{4} = 1\]

\[y_{1} = 2 \cdot 2,5 - 7 = 5 - 7 = - 2;\ \ \ \ \ \]

\[\ y_{2} = 2 \cdot 1 - 7 = 2 - 7 = - 5.\]

\[Ответ:(2,5;\ - 2);\ \ (1;\ - 5).\]