Systems Lab
Drag both lines with the sliders and watch the intersection — the solution — move, merge, or vanish as the system changes classification.
1 Systems Lab
Four sliders, two lines. The gold dot is the solution — watch what happens when the lines go parallel.
One solution
2 What to notice
Three experiments.
1. Make them parallel
Set both slopes to 1 with different intercepts: the gold dot vanishes — no solution.
2. Make them coincide
Set both slopes AND both intercepts equal: the lines overlap — infinitely many solutions.
3. Chase the dot
With slopes 1 and −1, slide b2: the solution glides along line 1. The solution always satisfies both.