При каком значении p график уравнения y+px=0 пройдет через точку пересечения прямых y=5/9x-16 и y=3/4x+5?

\[\left\{ \begin{matrix}
y = \frac{5}{9}x - 16 \\
y = \frac{3}{4}x + 5\ \ \\
\end{matrix} \right.\ \]

\[1)\frac{5}{9}x - 16 = \frac{3}{4}x + 5\]

\[\frac{5}{9}x - \frac{3}{4}x = 5 + 16\]

\[\frac{20 - 27}{36}x = 21\]

\[- \frac{7}{36}x = 21\ \ \ \ | \bullet \frac{36}{7}\]

\[x = - 3 \bullet 36\]

\[x = - 108.\]

\[2)\ y = \frac{5}{9} \bullet ( - 108) - 16\]

\[y - - 60 - 16\]

\[y = - 76.\]

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

\[- 76 + p \bullet ( - 108) = 0\]

\[- 108p = 76\]

\[p = - \frac{76}{108}\]

\[p = - \frac{19}{27}\]

\[Ответ:\ \ при\ \ p = - \frac{19}{27}.\]