Linear Equation Solver

Linear Equation Solver is evaluated from a, b and c. The calculation reports Solution x, Solution Type and Verification.

Results

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About the Linear Equation Solver

Linear Equation Solver is treated here as a quantitative relation between a, b, c and d and Solution x, Solution Type and Verification.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
ax + b = cx + d → x = (d - b) / (a - c) [when a ≠ c]

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

ax + b = cx + d → x = (d - b) / (a - c) [when a ≠ c]

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Simple One-Step — Budget Problem

Inputs

a: 1 b: 0 c: 0 d: 250
Solution x: 250. Solution Type: Unique solution: x = 250. Verification: 250

With a = 1, b = 0, c = 0 and d = 250 as the stated inputs, the result is Solution x = 250, Solution Type = Unique solution: x = 250 and Verification = 250. Each value corresponds to the declared output fields.

Example 2: Break-Even Units

Inputs

a: 25 b: 0 c: 15 d: 400
Solution x: 40. Solution Type: Unique solution: x = 40. Verification: 1,000

With a = 25, b = 0, c = 15 and d = 400 as the stated inputs, the result is Solution x = 40, Solution Type = Unique solution: x = 40 and Verification = 1,000. Each value corresponds to the declared output fields.

Example 3: Temperature Conversion Equality

Inputs

a: 1 b: 0 c: 0.5556 d: -17.78
Solution x: -40.0090009. Solution Type: Unique solution: x = -40.0090009. Verification: -40.009001

With a = 1, b = 0, c = 0.5556 and d = -17.78 as the stated inputs, the result is Solution x = -40.0090009, Solution Type = Unique solution: x = -40.0090009 and Verification = -40.009001. Each value corresponds to the declared output fields.

Example 4: No Solution — Contradictory Constraints

Inputs

a: 3 b: 7 c: 3 d: 10
Solution Type: No solution (contradiction - equation is never true)

With a = 3, b = 7, c = 3 and d = 10 as the stated inputs, the result is Solution Type = No solution (contradiction - equation is never true). Each value corresponds to the declared output fields.

Common Use Cases

  • Solve 3x + 5 = 20 for x
  • Solve equations with x on both sides
  • Check if a linear equation has one, zero, or infinite solutions
  • Find breakeven quantity in business