CalculateMeasure

Math & Geometry

System of Equations 3x3 Calculator

Solve three linear equations in three unknowns using determinants.

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Calculator guide

How to use the System of Equations 3x3 Calculator

Solve three linear equations in three unknowns using determinants. Enter the requested values and select Calculate. The result and supporting values are produced locally in your browser.

Formula

Solve A·[x y z]ᵀ = b using Cramer’s rule when det(A) ≠ 0

Worked example

The system x + y + z = 6, 2x − y + z = 3, and x + 2y − z = 3 has a unique solution.

What to keep in mind

  • A zero determinant means the system has no unique solution.

Methodology

This calculator uses deterministic arithmetic and performs the calculation locally in your browser. Verify assumptions, units, and source values for your specific use case.

Review standard: Level A · Standard formula. How calculator reviews work.

Frequently asked questions

What does this calculator calculate?

Solve three linear equations in three unknowns using determinants.

How is the result calculated?

Solve A·[x y z]ᵀ = b using Cramer’s rule when det(A) ≠ 0.

Can I use the result for an important decision?

Use the result as a calculation aid and verify the inputs, assumptions, and applicable professional or regulatory requirements before relying on it for an important decision.

Does CalculateMeasure store the values I enter?

The calculator performs its arithmetic in your browser. The calculator itself does not need to send your entered values to a server to produce the result.