Given the inconsistent system of linear equations
$$ y = 3x-1 $$
$$ y = 3x+1 $$
What sort of properties could be expressed about the system, other than the obvious like "the lines are parallel, slope is equal," etc.?
The direction I'm going here is that it seems there is some way to express this as one function like $f(b)=3x+b$ where $b= \pm 1$, but that obviously can't graph correctly, since there is no $y$ involved. Any ideas?