Решите систему уравнений: y-5x=13; y^2-13x=23.

Ответ:

\[\left\{ \begin{matrix} y - 5x = 1\ \ \ \ \ \ \ \\ y^{2} - 13x = 23 \\ \end{matrix} \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} y = 5x + 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (5x + 1)^{2} - 13x = 23 \\ \end{matrix} \right.\ \]

\[25x^{2} + 10x + 1 - 13x - 23 = 0\]

\[25x^{2} - 3x - 22 = 0\]

\[D_{1} = 9 + 2200 = 2209 = 47^{2}\]

\[x_{1} = \frac{3 + 47}{50} = 1;\]

\[x_{2} = \frac{3 - 47}{50} = - \frac{44}{50} =\]

\[= - \frac{88}{100} = - 0,88.\]

\[y_{1} = 5 \cdot 1 + 1 = 6;\]

\[y_{2} = 5 \cdot ( - 0,88) + 1 =\]

\[= - 4,4 + 1 = - 3,4.\]

\[Ответ:(1;6);( - 0,88; - 3,4).\]