Решите систему уравнений: 5x+y=14; 2x-3y=9.

Ответ:

\[\left\{ \begin{matrix} 5x + y = 14\ \ \ \ \ | \cdot 3 \\ 2x - 3y = 9\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 15x + 3y = 42 \\ 2x - 3y = 9\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ }( + )\]

\[17x = 51\]

\[x = 3.\]

\[\left\{ \begin{matrix} y = 14 - 5x \\ x = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = 14 - 15 \\ x = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = - 1 \\ x = 3\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(3; - 1).\]