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Elimination Method Calculator — result sheet
Solve a two-equation linear system by scaling and adding equations to eliminate the y variable, with the arithmetic shown.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Scale equation 1 by b₂ and equation 2 by −b₁, then add; x = (c₁b₂−c₂b₁)/(a₁b₂−a₂b₁) and y = (a₁c₂−a₂c₁)/(a₁b₂−a₂b₁).
The page follows the elimination or addition method: choose matching opposite y coefficients, add the equations, solve x, and substitute back for y. It leaves the original coefficients visible so every step can be checked.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Equation 1 x coefficient (a₁) — minimum -1000000000; maximum 1000000000
- Equation 1 y coefficient (b₁) — minimum -1000000000; maximum 1000000000
- Equation 1 right side (c₁) — minimum -1000000000; maximum 1000000000
- Equation 2 x coefficient (a₂) — minimum -1000000000; maximum 1000000000
- Equation 2 y coefficient (b₂) — minimum -1000000000; maximum 1000000000
- Equation 2 right side (c₂) — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Equation 1 x coefficient (a₁) | 2 |
| Equation 1 y coefficient (b₁) | 1 |
| Equation 1 right side (c₁) | 7 |
| Equation 2 x coefficient (a₂) | 1 |
| Equation 2 y coefficient (b₂) | -2 |
| Equation 2 right side (c₂) | 6 |
Scale and add to get x = 4, then substitute to get y = −1.
Assumptions and limits
- Equations are entered as a₁x + b₁y = c₁ and a₂x + b₂y = c₂.
- All inputs are finite real coefficients.
- The coefficient determinant must be nonzero for one unique ordered-pair answer.
- The method eliminates y; another elimination choice may be shorter on paper.
- The output is algebraic arithmetic and does not interpret a system's application context.
- A zero determinant is reported rather than silently dividing by 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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