Let $P,Q,R$ be ordered sets of $n$ points in $[0,1]$ e.g. $0 \leq p_1 < p_2 < \ldots < p_{n-1} < p_n \leq 1$. Let $\mathbf{u},\mathbf{v},\mathbf{w}$ be pairwise non-colinear plane vectors and $\mathbf{u}^\perp,\mathbf{v}^\perp,\mathbf{w}^\perp$ their respective perpendicular vectors. Consider the...

I think the status quo is fine. Linear systems of equations can belong in either algebra-precalculus or linear-algebra, depending on the techniques and tools the student knows and is expected to use. A linear-equations tag would probably draw traffic from the whole spectrum (not only about $2x+8=...