Решите систему уравнений: 2x/3-2+y/2; 2x/3+y=8.

\[\left\{ \begin{matrix}
\frac{2x}{3} = 2 + \frac{y}{2}\ \ \ \ | \cdot 6 \\
\frac{2x}{3} + y = 8\ \ \ \ | \cdot 3 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
2 \cdot 2x = 6 \cdot 2 + 3y \\
2x + 3y = 3 \cdot 8\ \ \ \ \ \\
\end{matrix} \right.\ \]

\[\left\{ \begin{matrix}
4x - 3y = 12\ \ \ (1) \\
2x + 3y = 24\ \ \ (2) \\
\end{matrix} \right.\ \]

\[6x = 36\ \ \]

\[x = 6\]

\[\left\{ \begin{matrix}
x = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
4x - 3y = 12 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
3y = 4x - 12 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
x = 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\
y = \frac{4}{3} \cdot 6 - 4\ \\
\end{matrix} \right.\ \text{\ \ \ \ }\]

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

\[Ответ:(6;4).\]