Subst eqn line BA with eqn line BC to get intersection of point B.

LockB, in short, lines AB and BC intersect at one point. And that is at point B.

Just as a pair of non-parallel simultaneous equations in two unknowns can get us one solution for x and y, so do two lines intersecting at a common point.

By analogy, we can do a simul on the equations to find what B are (the lines are never going to intersect elsewhere again).

if theres 2 equation intersecting we can only use the equations to find the point that intersects (B) but cannot find the other points that are not intersecting (A and C)?

Sadly yes. That’s the case. We can only deduce the intersecting point from two equations.