Other possible point of view: with $n = (1, -3)^\top$, the equation you are trying to solve is: $$ ll p \in bb{R},^2, le a f(p), n le = 0$$ So it would make perfect sense to express $p$ in a basis $(n, t)$ where $t n$ (or at least, not colinear).
I saw that solution on the net, but I can't understand it. I think I'm messing a geometry chapter.