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Substitution Method Calculator — result sheet
Solve a two-equation linear system by isolating y in the first equation, substituting into the second, and checking the ordered pair.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Solve equation 1 as y=(c₁−a₁x)/b₁, substitute into equation 2, then solve x and back-substitute for y.
This method turns one equation into an expression for y and replaces y in the other equation. The result is a one-variable equation followed by a visible back-substitution and two-equation check.
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 |
Equation 1 gives y = 7 − 2x; substitution gives x = 4 and y = −1.
Assumptions and limits
- Equations are entered as a₁x + b₁y = c₁ and a₂x + b₂y = c₂.
- Equation 1 must have a nonzero y coefficient so y can be isolated.
- The substituted one-variable coefficient must be nonzero for one unique solution.
- All inputs are finite real coefficients.
- The output uses equation 1 as the expression source by design.
- A zero reduced coefficient is reported rather than returning a division-by-zero result.
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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