1. The problem statement, all variables and given/known data What does it mean that basic arithmetic can be performed with two (non parallel) linear equations and that the resulting equation also intersects the same point? Proof and or anecdotal explanation would be much appreciated. 2. Relevant equations If (α) 3y = 4x + 1 (β) 2y = -x -2 Then aα + bβ = λ And there exists x such that α(x) = β(x) = γ(x) 3. The attempt at a solution 1. If a,b are constant then n(y=ax+b) is logically equivalent to y=ax+b [itex]\forall[/itex]line for all n. 2. The family of equations given by y=n(ax+b)+c all rotate about a point given as follows: x coordinate given by assuming n=1 and solving for x. y coordinate given by y=c (in other words assume n=0).