Cramers Rule Calculator

Cramer's Rule Calculator

Solve 2×2 and 3×3 systems of linear equations using Cramer's Rule.

Last updated: June 2026 | By Patchworkr Team

System Solver

Coefficients and constants

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Fill every field with a finite number before solving.

Results

Press Solve to calculate the determinants and the solution.
Cramer's Rule uses the determinant of the coefficient matrix and one replaced column per variable.

What does it solve?

Cramer's Rule solves systems of linear equations by dividing determinant replacements by the determinant of the coefficient matrix.

How to Use It

  1. Choose 2×2 or 3×3.
  2. Enter the coefficients and constants.
  3. Press Solve and read the determinants plus the solution.

What if det(A) is zero?

Cramer's Rule does not produce a unique solution when the coefficient determinant is zero.

Can I use decimals?

Yes. The fields accept finite decimal and scientific-notation values.

What if I leave a field blank?

Blank fields are rejected before solving.

Why show the determinants?

They let you verify the computation rather than trusting the final answer blindly.

Formula

x = det(X) / det(A), y = det(Y) / det(A), z = det(Z) / det(A)

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