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Two-by-Two Cramer’s Rule Calculator — result sheet
Solve a two-equation linear system with Cramer’s rule and show its determinant condition.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: D=ad−bc; x=(ed−bf)/D; y=(af−ec)/D.
The determinant is checked before division, so parallel or dependent equations are not presented as a unique solution.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Coefficient a — minimum -1000000; maximum 1000000
- Coefficient b — minimum -1000000; maximum 1000000
- Coefficient c — minimum -1000000; maximum 1000000
- Coefficient d — minimum -1000000; maximum 1000000
- Right side e — minimum -1000000; maximum 1000000
- Right side f — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Coefficient a | 2 |
| Coefficient b | 1 |
| Coefficient c | 1 |
| Coefficient d | 3 |
| Right side e | 5 |
| Right side f | 7 |
x =1.6; y =1.8; determinant =5.
Assumptions and limits
- The system is ax+by=e and cx+dy=f with finite real coefficients.
- A nonzero determinant is required for the unique Cramer solution.
- No symbolic parameter case is inferred when the determinant is zero.
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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