Решите систему уравнений: 1/5*(x+y)=2; 1/2*(x-y)=1.

Ответ:

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

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

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

\[\left\{ \begin{matrix} x = 10 - y \\ - 2y = - 8\ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

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

\[\left\{ \begin{matrix} y = 4 \\ x = 6 \\ \end{matrix} \right.\ \]

\[Ответ:(6;4).\]