При каком значении p график уравнения y+px=0 пройдет через точку пересечения прямых y=2/7x-21 и y=-1/9x+29?

\[\left\{ \begin{matrix} y = \frac{2}{7}x - 21\ \ \ \ \\ y = - \frac{1}{9}x + 29 \\ \end{matrix} \right.\ \]

\[1)\ \frac{2}{7}x - 21 = - \frac{1}{9}x + 29\]

\[\frac{2}{7}x + \frac{1}{9}x = 29 + 21\]

\[\frac{18 + 7}{63}x = 50\]

\[\frac{25}{63}x = 50\ \ \ \ \ \ | \bullet \frac{63}{25}\]

\[x = 63 \bullet 2\]

\[x = 126.\]

\[2)\ y = - \frac{1}{9} \bullet 126 + 29\]

\[y = - 14 + 29\]

\[y = 15.\]

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

\[15 + p \bullet 126 = 0\]

\[126p = - 15\]

\[p = - \frac{15}{126}\]

\[p = - \frac{5}{42}.\]

\[Ответ:\ - \frac{5}{42}.\]