basic

Cramer's Rule 2×2 Linear System Calculator

x = D_x/D; y = D_y/D; D = ad − bc.

Solves a system of two linear equations ax+by=e, cx+dy=f using Cramer's Rule. Computes the main determinant D and solution determinants D_x and D_y.

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

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Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

D = ad−bc; D_x = ed−bf; D_y = af−ce; x = D_x/D; y = D_y/D

In depth

Solves a system of two linear equations ax+by=e, cx+dy=f using Cramer's Rule. Computes the main determinant D and solution determinants D_x and D_y.