Решите систему уравнений: 1/x+1/y=5/6; 2y-x=1.

Ответ:

\[\left\{ \begin{matrix} x = 2y - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 6y + 6 \cdot (2y - 1) = 5y(2y - 1) \\ \end{matrix} \right.\ \ \]

\[6y + 12y - 6 = 10y^{2} - 5y\]

\[10y^{2} - 5y - 18y + 6 = 0\]

\[10y^{2} - 23y + 6 = 0\]

\[D = 529 - 240 = 289 = 17^{2}\]

\[y_{1} = \frac{23 + 17}{20} = 2;\ \ \ \]

\[y_{2} = \frac{23 - 17}{20} = \frac{6}{20} = 0,3.\]

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

\[x_{2} = 2 \cdot 0,3 - 1 = - 0,4.\]

\[Ответ:(3;2);( - 0,4;0,3).\]