What quantity did you change?
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.
Labs / Mathematics / Systems of Equations
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.
Why it matters
Why explore this?
Mathematics helps us describe patterns precisely and predict what comes next. This model turns an abstract relationship into something you can change and observe.
Explore
Try the model
solution —type one solutionlines intersecting
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
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?
Explain
Make sense of what happened
State the pattern in words, test it with another example, and then connect it to the mathematical rule or representation shown in the model.
Check
Before you leave
What pattern did you observe?
Does the pattern work for another example?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.