Решите систему уравнений: 2*(x+y)^2-7*(x+y)+3=0; 2x-3y=-1.

\[\left\{ \begin{matrix} 2 \cdot (x + y)^{2} - 7 \cdot (x + y) + 3 = 0\ (*) \\ 2x - 3y = - 1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[*D = 49 - 24 = 25\]

\[(x + y)_{1,2} = \frac{7 \pm 5}{4} = 0,5;\ \ 3.\]

\[1)\ \left\{ \begin{matrix} x + y = 0,5\ \ \ \ \ \ | \cdot 2 \\ 2x - 3y = - 1\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 2x + 2y = 1\ \ \ \\ 2x - 3y = - 1 \\ \end{matrix} \right.\ \ \ ( - )\]

\[5y = 2\]

\[y = \frac{2}{5} = 0,4.\]

\[x = 0,5 - y = 0,1.\]

\[2)\ \left\{ \begin{matrix} x + y = 3\ \ \ \ \ \ | \cdot 2 \\ 2x - 3y = - 1\ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 2x + 2y = 6\ \ \ \ \\ 2x - 3y = - 1 \\ \end{matrix} \right.\ \ \ ( - )\]

\[5y = 7\]

\[y = \frac{7}{5} = 1,4.\]

\[x = 3 - y = 3 - 1,4 = 1,6.\]

\(Ответ:(0,1;0,4)\ \ или\ \ (1,6;\ 1,4).\)