Решите систему уравнений: x^2+y^2+2xy=100; y-x=6.

\[\left\{ \begin{matrix} x^{2} + y^{2} + 2xy = 100 \\ y - x = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} (x + y)^{2} = 100 \\ y - x = 6\ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[1.\ \left\{ \begin{matrix} x + y = 10 \\ y - x = 6\ \ \\ \end{matrix}\text{\ \ } \right.\ ( + )\text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} 2y = 16\ \ \ \ \ \\ x = 10 - y \\ \end{matrix}\text{\ \ \ \ \ } \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} y = 8 \\ x = 2 \\ \end{matrix} \right.\ \]

\[2.\ \left\{ \begin{matrix} x + y = - 10 \\ y - x = 6\ \ \ \ \ \\ \end{matrix}\text{\ \ } \right.\ ( + )\text{\ \ }\]

\[\left\{ \begin{matrix} 2y = - 4\ \ \ \ \ \ \ \ \\ x = - 10 - y \\ \end{matrix}\text{\ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} y = - 2 \\ x = - 8 \\ \end{matrix} \right.\ \]

\[Ответ:(2;8);\ ( - 8;\ - 2)\text{.\ }\]