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3x3 Linear System Solver — result sheet
Solve three equations in x, y, z with Cramer's rule.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: x = Dx/D; y = Dy/D; z = Dz/D with 3x3 determinants.
Each variable's determinant swaps in the right-hand column. A zero main determinant means no unique solution and is rejected with an explanation.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Row 1: x, y, z, rhs — Four numbers: coefficients then right side.
- Row 2: x, y, z, rhs — Four numbers.
- Row 3: x, y, z, rhs — Four numbers.
Worked example
| Input | Value |
|---|---|
| Row 1: x, y, z, rhs | 1, 1, 1, 6 |
| Row 2: x, y, z, rhs | 2, -1, 1, 3 |
| Row 3: x, y, z, rhs | 1, 2, -1, 2 |
x = 1; y = 2; z = 3.
Assumptions and limits
- Linear equations in x, y, z; 4 finite numbers per row.
- Nonzero determinant required.
- Real 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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