Labs / Mathematics
Systems of Equations
Each line is one equation; where they cross is the pair of numbers that makes both true at once. Drag a line or nudge the sliders, and turn on the elimination steps to see the algebra that finds the same point.
solution —type one solutionlines intersecting
What to try
- Make both slopes equal but keep the intercepts different. Where did the solution go, and why does the algebra end in something impossible?
- Now match the intercepts too. How can two equations suddenly have infinitely many solutions?
- Slide slope 2 slowly toward slope 1. What happens to the intersection point as the lines get closer to parallel?
- Press "Snap to integer solution." Which numbers changed, and which stayed the same, to land the crossing on a grid corner?
- Can you find two different systems that share the exact same solution point but look nothing alike?