CalculateMeasure

Math & Geometry

System of Equations 2x2 Calculator

Solve two linear equations in two unknowns using determinants.

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Calculator guide

How to use the System of Equations 2x2 Calculator

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

Formula

For a₁x + b₁y = c₁ and a₂x + b₂y = c₂: x = (c₁b₂ − b₁c₂)/D, y = (a₁c₂ − c₁a₂)/D, D = a₁b₂ − b₁a₂

Worked example

For 2x + y = 5 and x − y = 1, the solution is x = 2 and y = 1.

What to keep in mind

  • A zero determinant indicates no unique solution (parallel/dependent equations).

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 two linear equations in two unknowns using determinants.

How is the result calculated?

For a₁x + b₁y = c₁ and a₂x + b₂y = c₂: x = (c₁b₂ − b₁c₂)/D, y = (a₁c₂ − c₁a₂)/D, D = a₁b₂ − b₁a₂.

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.