What quantity did you change?
Labs / Mathematics
Solving Linear Systems
A system of equations and its augmented matrix sit side by side. Press Step (or Auto-run) to apply one elementary row operation at a time — swapping, scaling, and subtracting rows — until the matrix collapses to reduced row-echelon form and the answer just falls out. For a 2×2 system, each equation is a line, and the solution is exactly where the two lines cross.
Labs / Mathematics / Solving Linear Systems
Solving Linear Systems
A system of equations and its augmented matrix sit side by side. Press Step (or Auto-run) to apply one elementary row operation at a time — swapping, scaling, and subtracting rows — until the matrix collapses to reduced row-echelon form and the answer just falls out. For a 2×2 system, each equation is a line, and the solution is exactly where the two lines cross.
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
step 0 / 0op —solution —cursor —
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- In the "No solution" system, watch the matrix. What does the row that becomes 0 = a nonzero number tell you about the two lines?
- For "Infinite" solutions, why do the two lines land exactly on top of each other, and how does the matrix reveal that a variable is free?
- Switch between 2×2 and 3×3 — does adding a third equation always pin down a single point, or can it still fail?
- Hit Randomize a few times. Can you predict from the equations alone whether you'll get one answer, none, or infinitely many before you step through?
- Does the order in which you clear the columns change the final answer, even though the intermediate matrices look different?
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.