\[\left\{ \begin{matrix} y = \frac{5}{9}x - 16 \\ y = \frac{3}{4}x + 5\ \ \\ \end{matrix} \right.\ \]
\[1)\frac{5}{9}x - 16 = \frac{3}{4}x + 5\]
\[\frac{5}{9}x - \frac{3}{4}x = 5 + 16\]
\[\frac{20 - 27}{36}x = 21\]
\[- \frac{7}{36}x = 21\ \ \ \ | \bullet \frac{36}{7}\]
\[x = - 3 \bullet 36\]
\[x = - 108.\]
\[2)\ y = \frac{5}{9} \bullet ( - 108) - 16\]
\[y - - 60 - 16\]
\[y = - 76.\]
\[3)\ y + px = 0\]
\[- 76 + p \bullet ( - 108) = 0\]
\[- 108p = 76\]
\[p = - \frac{76}{108}\]
\[p = - \frac{19}{27}\]
\[Ответ:\ \ при\ \ p = - \frac{19}{27}.\]