What is the answer for 3p+4q+1=0 5p+6q-3=0

3p+4q+1=0

 5p+6q-3=0

$\small{ \begin{array}{lrcll} (1) & 3p+4q+1 &=& 0 \qquad & | \qquad \cdot 3 \\ & 9p+12q+3 &=& 0 \\ \hline (2) & 5p+6q-3 &=& 0 \qquad & | \qquad \cdot 2 \\ & 10p+12q-6 &=& 0 \\ \\ \hline \\ (1) & 9p+12q+3 &=& 0 \\ (2) & 10p+12q-6 &=& 0 \\ \hline (2)-(1) & 10p -9p + 12q-12q-6-3 &=& 0 \\ & 10p -9p -6-3 &=& 0 \\ & 10p -9p -9 &=& 0 \\ & p -9 &=& 0 \\ & \mathbf{p} & \mathbf{=} & \mathbf{9} \\ \hline & 3p + 4q + 1 &=& 0 \qquad & | \qquad p = 9\\ & 3\cdot 9 + 4q + 1 &=& 0 \\ & 27 + 4q + 1 &=& 0 \\ & 4q + 28 &=& 0 \qquad & | \qquad :4\\ & q + 7 &=& 0 \\ & \mathbf{q} &\mathbf{=}& \mathbf{-7} \\ \end{array} }$