При каком значении p график уравнения y+px=0 пройдет через точку пересечения прямых y=-7/8x+17 и y=-3/5x-16?

\[\left\{ \begin{matrix}
y = - \frac{7}{8}x + 17 \\
y = - \frac{3}{5}x - 16 \\
\end{matrix} \right.\ \]

\[1) - \frac{7}{8}x + 17 = - \frac{3}{5}x - 16\]

\[- \frac{7}{8}x + \frac{3}{5}x = - 16 - 17\]

\[\frac{- 35 + 24}{40}x = - 33\ \ \ | \bullet 40\]

\[- 11x = - 1320\ \ \ |\ :( - 11)\]

\[x = 120.\]

\[2)\ y = - \frac{3}{5} \bullet 120 - 16\]

\[y = - 3 \bullet 24 - 16\]

\[y = - 72 - 16\]

\[y = - 88.\]

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

\[- 88 + p \bullet 120 = 0\]

\[120p = 88\]

\[p = \frac{88}{120}\]

\[p = \frac{22}{30}\]

\[p = \frac{11}{15}\]

\[Ответ:\ \ при\ p = \frac{11}{15}.\]