basic

System of Linear Equations Solver (2×2)

Solve { a₁x + b₁y = c₁; a₂x + b₂y = c₂ } via Cramer's rule.

Solve a 2×2 system of linear equations { a₁x + b₁y = c₁ ; a₂x + b₂y = c₂ } using Cramer's rule, with a determinant check that flags singular systems.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

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 = a₁b₂ − a₂b₁. x = (c₁b₂ − c₂b₁) / D. y = (a₁c₂ − a₂c₁) / D.

In depth

Solve a 2×2 system of linear equations { a₁x + b₁y = c₁ ; a₂x + b₂y = c₂ } using Cramer's rule, with a determinant check that flags singular systems.