При каком значении p график уравнения y+px=0 пройдет через точку пересечения прямых y=-3/8x+15 и y=5/6x+73?

\[\left\{ \begin{matrix} y = - \frac{3}{8}x + 15 \\ y = \frac{5}{6}x + 73\ \ \ \ \\ \end{matrix} \right.\ \]

\[1)\ - \frac{3}{8}x + 15 = \frac{5}{6}x + 73\]

\[- \frac{3}{8}x - \frac{5}{6}x = 73 - 15\]

\[- \frac{9 + 20}{24}x = 58\ \ \ \ \ \ | \bullet 24\]

\[- 29x = 1392\ \ \ \ |\ :( - 29)\]

\[x = - 48.\]

\[2)\ y = \frac{5}{6} \bullet ( - 48) + 73\]

\[y = - 5 \bullet 8 + 73\]

\[y = 73 - 40\]

\[y = 33.\]

\[3)\ y + px = 0\]

\[33 + p \bullet ( - 48) = 0\]

\[48p = 33\]

\[p = \frac{33}{48}\]

\[p = \frac{11}{16}.\]

\[Ответ:\ \ при\ p = \frac{11}{16}.\]