Решите систему уравнений:5x-2y=0; 2x-5y=-21.

\[\left\{ \begin{matrix}
5x - 2y = 0\ \ \ \ \ \ \ \ \ \ | \cdot 2\ \ \ \ \ \ \\
2x - 5y = - 21\ \ \ | \cdot ( - 5) \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
10x - 4y = 0\ \ \ \ \ \ \ \ \ \ \ \ (1) \\
- 10x + 25y = 105\ \ \ (2) \\
\end{matrix} \right.\ \]

\[21y = 105\ \ \]

\[y = 5\]

\[\left\{ \begin{matrix}
y = 5\ \ \ \ \ \ \ \ \ \ \ \ \\
5x - 2y = 0 \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
y = 5\ \ \ \ \ \ \\
5x = 2y\ \\
\end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix}
y = 5\ \ \ \ \\
x = \frac{2}{5}y \\
\end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix}
y = 5\ \ \ \ \ \ \\
x = \frac{2}{5} \cdot 5\ \\
\end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix}
y = 5 \\
x = 2 \\
\end{matrix} \right.\ \]

\[Ответ:(2;5).\]