Two straight lines on one grid. Every point on a line is a pair (x, y) that makes that equation true. So the single point where the lines cross is the one (x, y) that makes both true at once — the solution of the system.
Slide a line 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 lines are the picture of "0 = 1": equations that can't both be satisfied.
Keep sliding until the two lines land exactly on top of each other. Now every point is on both — the system has infinitely many solutions. It was really one equation written twice.
That's the whole story: two lines meet once (one solution), never (none), or everywhere (infinitely many). Solving by algebra just finds which case you're in without drawing.
Something in the simulation stopped unexpectedly — the lesson continues without it. Nothing you did was wrong; you can move on.