How to use the system of two linear equations calculator
Solve two equations with two unknowns using Cramer's rule. Enter a₁, b₁, c₁, a₂, b₂, c₂ in the fields above; the determinant, x, y are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- a1 — a₁
- b1 — b₁
- c1 — c₁
- a2 — a₂
- b2 — b₂
- c2 — c₂
Worked example
With a₁ = 2, b₁ = 3, c₁ = 13, a₂ = 1, b₂ = -1, c₂ = 1, the calculator gives determinant ≈ -5; x ≈ 3.2; y ≈ 2.2.
Frequently asked questions
What is the formula for the system of two linear equations calculation?
Determinant = a1 × b2-a2 × b1. x = (c1 × b2-c2 × b1) / [Determinant]. y = (a1 × c2-a2 × c1) / [Determinant]. Here a1 is a₁, b1 is b₁, c1 is c₁, a2 is a₂, b2 is b₂, c2 is c₂.
What inputs do I need for the system of two linear equations solver calculator?
You need a₁, b₁, c₁, a₂, b₂, c₂. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.