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

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

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

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

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

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

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

\[Ответ:(6;4).\]