Решите систему уравнений: 2x+y=7; 1/x-1/y=1/6.

\[6 \cdot ( - 2x + 7) - 6x =\]

\[= x( - 2x + 7)\]

\[- 12x + 42 - 6x = - 2x^{2} + 7x\]

\[2x^{2} - 18x - 7x + 42 = 0\]

\[2x^{2} - 25x + 42 = 0\]

\[D = ( - 25)^{2} - 4 \cdot 2 \cdot 42 =\]

\[= 625 - 336 = 289;\ \ \ \ \sqrt{D} = 17.\]

\[x_{1} = \frac{25 + 17}{2 \cdot 2} = \frac{42}{4} = \frac{21}{2} = 10,5\]

\[x_{2} = \frac{25 - 1}{2 \cdot 2} = \frac{8}{4} = 2\]

\[y_{1} = - 2 \cdot 10,5 + 7 = - 14\]

\[y_{2} = - 2 \cdot 2 + 7 = - 4 + 7 = 3\]

\[Ответ:(10,5;\ - 14);\ \ (2;3).\]