Two straight roads across one map. Every point on a road is a pair (x, y) that makes that road's equation true. So the one place where the roads cross — the junction — is the one (x, y) that satisfies both at once: the solution of the system. Watch the two cars: the junction is the only spot where they can ever meet.
Turn a road until its slope matches the other's and they run side by side, never touching. Now there is no point on both — the system has no solution. Parallel roads are the picture of "0 = 1": equations that can't both be satisfied.
Keep sliding until the two roads lie exactly on top of each other. Now every point is on both — the system has infinitely many solutions. It was really one road drawn twice.
That's the whole story: two roads meet once (one solution), never (none), or everywhere (infinitely many). Solving by algebra just finds which case you're in without drawing the map.
Something in the simulation stopped unexpectedly — the lesson continues without it. Nothing you did was wrong; you can move on.