How this calculator works
For ax + by = c and dx + ey = f, use the non-zero determinant ae - bd to compute x and y.
Formula
x=(ce-bf)/(ae-bd), y=(af-cd)/(ae-bd)Solves ax + by = c and dx + ey = f using the non-zero 2×2 determinant.
Worked example
x+y=5; x-y=1 is a verified test case used by the calculation engine.
Assumptions and limitations
- The two equations must have one unique solution.
- Inputs are finite real numbers.
Methodology & sources
This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.
- CalcuMint deterministic algebra engine — Standard two-variable linear-system identities.
Frequently asked questions
What systems are supported?
This version solves two linear equations in two variables with a unique solution.
What happens for dependent or inconsistent equations?
A zero determinant is rejected because the system does not have one unique solution.