System Equations
Solve 2x2 and 3x3 linear systems with step-by-step Gaussian elimination. Enter coefficients and get unique, infinite, or no-solution results in your browser.
Solve small linear systems step by step
Enter coefficients for two or three equations in standard form \(a_1 x + a_2 y + \cdots = b\). The solver applies Gaussian elimination, shows the reduced matrix, and reports whether the system has a unique solution, no solution, or infinitely many solutions.
Related algebra tools
Row-reduce larger matrices with the Row Echelon Form Calculator, find determinants using the Matrix Determinant Calculator, or practice quadratics with the Quadratic Calculator.
Frequently Asked Questions
Which system sizes are supported?
You can solve 2×2 and 3×3 linear systems with real coefficients.
What does infinitely many solutions mean?
It means the equations describe the same line or plane with redundant information. The tool stops after detecting dependence.
Can I enter fractions?
Yes. Type decimal forms of fractions (for example 0.5 for one half).
How are steps formatted?
Each elimination step is listed in plain language so you can compare with homework or classroom notation.
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