Coinciding Linear Equations Contradiction

For two lines to coincide, the ratio of coefficients must be equal: $\frac{3}{q} = \frac{21}{r} = \frac{p}{-7} = k \neq 0$. Thus, $q = \frac{3}{k}, r = \frac{21}{k}, p = -7k$. Note that $\frac{r}{q} = 7$, so $r = 7q$. If $q > 0$, then $r = 7q > q$, so $q$ cannot be the largest among $p, q, r$. If $q < 0$, then $r = 7q < q$, but $p = -7k = -7(3/q) = -21/q > 0$, so $p$ is positive and thus $p > q$, which again means $q$ cannot be the largest. Therefore, $q$ can NEVER be the largest among $p, q, r$. Saying "The largest among $p, q,$ and $r$ is $q$" definitely contradicts the fact that the lines coincide.