Решите систему уравнений 5x-3y=21; 3x+2y=5.

Ответ:

\[\left\{ \begin{matrix} 5x - 3y = 21\ \ \ | \cdot 2 \\ 3x + 2y = 5\ \ \ \ \ | \cdot 3 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 10x - 6y = 42 \\ 9x + 6y = 15\ \ \\ \end{matrix} \right.\ ( + )\]

\[19x = 57\]

\[x = 3.\]

\[\left\{ \begin{matrix} x = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2y = 5 - 3x \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 3\ \ \ \ \ \ \ \ \ \ \\ 2y = 5 - 9 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 3\ \ \ \ \ \ \\ 2y = - 4 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 3\ \ \ \\ y = - 2 \\ \end{matrix} \right.\ \]

\[Ответ:(3;\ - 2).\]