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

Ответ:

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

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

\[21y = 105\ \ \]

\[y = 5\]

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

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

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

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

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

\[Ответ:(2;5).\]