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Linear Systems Solver (2×2 / 3×3)

Solve 2×2 or 3×3 linear systems with Gaussian elimination and review solution classification, parametric forms, residuals, and elimination steps in one place.

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Educational use only. Double-check symbolic work when required.

How to use (3 steps)

  1. Choose 2×2 or 3×3 and pick Equation input or Matrix input. Load a sample from the Examples menu if you want to see a ready-made system.
  2. Enter your equations or the augmented matrix coefficients carefully (one row per equation).
  3. Press Solve to see the solution and, if enabled, elimination steps. Adjust the “Prefer fractional output” and “Show elimination steps” options as needed.

Use this as a learning aid; always write up final work in the format your course requires.

Dimension

FAQ

How does the solver classify the system?

It computes the ranks of A and [A|b] with RREF. If rank(A) = rank([A|b]) = n the solution is unique; if rank(A) = rank([A|b]) < n there are infinitely many solutions; if rank(A) < rank([A|b]) the system is inconsistent.

Can I switch between equation and matrix input?

Yes. Enter equations such as 2x+3y=7 or fill the matrix directly. Examples populate both views and you can share the current setup through the URL.

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