MihsabaHow to use
This tool solves a 2×2 or 3×3 linear system. It uses Gaussian elimination with partial pivoting for numerical stability, then distinguishes a unique solution from an inconsistent system or a system with infinitely many solutions.
- Choose 2×2 or 3×3.
- Enter each equation's variable coefficients and right-hand constant; in 2×2 mode only the first two variables and equations are used.
- Calculate to see the classification and, when unique, the variable values.
How it is calculated
Example
Example 2×2: 2x+y=5 and x−y=1. The unique solution is x=2 and y=1, which satisfies both equations.
Important notes
The calculator uses floating-point arithmetic, so nearly singular systems can be numerically sensitive. For safety-critical engineering or large systems, use specialized numerical software and inspect matrix conditioning.
Frequently asked questions
When are there infinitely many solutions?
When equations are dependent and the system remains consistent, leaving at least one free variable.
When is there no solution?
When elimination exposes a contradiction such as 0 equaling a non-zero value.
Does this use Cramer's rule?
No. It uses partial-pivot Gaussian elimination, a general approach for small systems.
Is this calculator free?
Yes. It is free to use and requires no account.