Answer:
p=1, q=-1
Step-by-step explanation:
[tex]\left\{\begin{aligned}2p+3q+1&=0\quad|\times5\\3p+5q+2&=0\quad|\times3\end{aligned}\right.\implies\left\{ -\begin{aligned}10p+15q+5&=0\\9p+15q+6&=0\end{aligned}\right.\implies p-1=0\implies \\\\\implies p=1\overset{\text{plug into first equation}}{\implies}2\times1+3q+1=0\implies 3q+3=0\implies \\\implies3q=-3\implies q=-1\implies \boxed{(p,\,q)=(1,\,-1)}[/tex]
