Вычислите координаты точки пересечения прямых: 4x-3y=-1 и 3x+2y=12.

Ответ:

\[4x - 3y = - 1\ \ \ и\ \ \ 3x + 2y = 12\]

\[\ \left\{ \begin{matrix} 4x - 3y = - 1\ \ | \cdot 2 \\ 3x + 2y = 12\ \ \ | \cdot 3 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} 8x - 6y = - 2\ \ \ (1) \\ 9x + 6y = 36\ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[17x = 34\]

\[x = 2\]

\[\left\{ \begin{matrix} x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x + 2y = 12 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2y = 12 - 3x \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 2\ \ \ \ \ \ \ \ \ \ \ \\ y = 6 - \frac{3}{2}x \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

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

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

\[Ответ:(2;3).\]