Cramer’s Rule Calculator (2×2 and 3×3 Systems, Free)

Use this free Cramer’s rule calculator to solve 2×2 and 3×3 systems of linear equations using determinants. Enter the coefficients and constants to get D, Dx, Dy (and Dz), the values of x, y, and z, a graph of the lines, and full step-by-step working.

How Cramer’s rule works

For a system written in standard form, compute the coefficient determinant D. Replace each variable’s column with the constants to get Dx, Dy, Dz, then divide: x = Dx/D, y = Dy/D, z = Dz/D. If D = 0, Cramer’s rule does not apply (no unique solution).

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How to use the calculator

1. Choose a 2×2 or 3×3 system.
2. Enter each coefficient and constant (negatives are fine).
3. Press Solve for the determinants and the solution.

Related: the System of Equations Calculator and the Matrix Calculator.

Frequently asked questions

What if the determinant D is zero?

Cramer’s rule needs D ≠ 0. If D = 0 the system has either no solution or infinitely many, and the calculator tells you so.

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Does it solve 3×3 systems?

Yes — switch to 3×3 to enter three equations; the tool computes D, Dx, Dy, Dz and x, y, z.

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Can I enter negative or decimal coefficients?

Yes, any real numbers work.

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