Number of Solutions to a System

The Desmos trick

Graph both equations in the system and literally count the intersection points. No crossings means no solution, one crossing means one solution, and if the two graphs completely overlap (you can only see one curve), the system has infinitely many solutions.

• Graph both equations in the same calculator and count where they cross
• Parallel lines that never touch mean 0 solutions
• If the graphs look identical and overlap completely, the system has infinitely many solutions