Question

For which values of P and Q does the following equation have infinitely many solutions?

Answer 1

$\bf Px+35=-6x+Q\implies \stackrel{P}{~~\begin{matrix} -6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}x+35=~~\begin{matrix} -6x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+\stackrel{Q}{35}\implies 35=35$

whenever you get an equality like so, that's a flat that both equations are exactly one and the same and thus the system has "infinitely many solutions".