\[\boxed{\mathbf{976.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[\mathbf{Дано:}\]
\[l_{1}:\ \ \ 4x + 3y - 6 = 0;\]
\[l_{2}:\ \ \ 2x + y - 4 = 0;\]
\[l_{1} \cap l_{2} = A.\]
\[\mathbf{Найти:}\]
\[A(x;y).\]
\[\mathbf{Решение.}\]
\[\left\{ \begin{matrix} 4x + 3y - 6 = 0\ \ \ \ \ \ \ \ \ \ \ \ \\ \left. \ 2x + y - 4 = 0 \right| \bullet ( - 2) \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 4x + 3y - 6 = 0\ \ \\ - 4x - 2y + 8 = 0 \\ \end{matrix} \right.\ ( + )\]
\[\ \left\{ \begin{matrix} y + 2 = 0\ \ \ \ \ \ \ \ \ \ \\ 2x + y - 4 = 0 \\ \end{matrix} \right.\ \text{\ \ \ }\]
\[\left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x - 2 - 4 = 0 \\ \end{matrix} \right.\ \text{\ \ \ }\]
\[\left\{ \begin{matrix} y = - 2 \\ 2x = 6 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = - 2 \\ x = 3\ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow A(3; - 2).\]
\[Ответ:\ A(3; - 2).\]