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

\[6 \cdot (2x - 1) + 6x = 5x(2x - 1)\]

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

\[10x^{2} - 5x - 12x - 6x + 6 = 0\]

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

\[D = ( - 23)^{2} - 4 \cdot 10 \cdot 6 =\]

\[= 529 - 240 = 289;\ \ \ \sqrt{D} = 17.\]

\[x_{1} = \frac{23 + 17}{2 \cdot 10} = \frac{40}{20} = 2;\ \ \ \ \ \ \ \ \ \]

\[\text{\ \ }x_{2} = \frac{23 - 17}{2 \cdot 10} = \frac{6}{20} = \frac{3}{10} = 0,3\]

\[y_{1} = 2 \cdot 2 - 1 = 4 - 1 = 3;\ \ \ \ \]

\[\ y_{2} = 2 \cdot 0,3 - 1 = 0,6 - 1 =\]

\[= - 0,4.\]

\[Ответ:(2;3);\ \ \ (0,3;\ - 0,4).\]