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2x2 Linear System Solver — result sheet
Solve two equations in two unknowns with Cramer's rule.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: det = a1*b2 - a2*b1; x = (c1*b2 - c2*b1)/det; y = (a1*c2 - a2*c1)/det.
Cramer's rule divides combination determinants by the coefficient determinant. A zero determinant means the lines are parallel or identical, so no unique solution exists and an error is reported.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- a1 (x in equation 1) — minimum -1000000000; maximum 1000000000
- b1 (y in equation 1) — minimum -1000000000; maximum 1000000000
- c1 (right side, equation 1) — minimum -1000000000; maximum 1000000000
- a2 (x in equation 2) — minimum -1000000000; maximum 1000000000
- b2 (y in equation 2) — minimum -1000000000; maximum 1000000000
- c2 (right side, equation 2) — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| a1 (x in equation 1) | 2 |
| b1 (y in equation 1) | 3 |
| c1 (right side, equation 1) | 7 |
| a2 (x in equation 2) | 1 |
| b2 (y in equation 2) | -1 |
| c2 (right side, equation 2) | 1 |
x = 2; y = 1.
Assumptions and limits
- Equations are linear in x and y.
- A zero determinant is rejected as having no unique solution.
- Real-number arithmetic only.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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