Linear Equations Calculator

Solve linear equations step-by-step. Analyze linear equations with detailed solutions and explanations.

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Equation: ax + b = 0

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About Linear Equations

What is a Linear Equation?

A linear equation is a first-degree polynomial equation of the form ax + b = 0, where a ≠ 0. Linear equations represent straight lines when graphed and have exactly one solution. They are fundamental in algebra and appear in many real-world applications: cost analysis, speed calculations, and simple relationships between variables.

Forms of Linear Equations

  • Standard Form: ax + b = 0
  • Slope-Intercept Form: y = mx + b
  • Point-Slope Form: y - y₁ = m(x - x₁)

How to Solve Linear Equations

  1. Isolate the variable: Move all terms containing x to one side
  2. Combine like terms: Simplify both sides of the equation
  3. Divide by coefficient: x = -b/a

Applications in Real Life

  • Economics: Cost analysis, profit calculations
  • Physics: Speed, distance, time relationships
  • Business: Pricing strategies, break-even analysis
  • Engineering: Simple mechanical systems, electrical circuits

Frequently Asked Questions

What if a = 0?

If a = 0, the equation becomes b = 0, which is either always true (if b = 0) or never true (if b ≠ 0).

How many solutions does a linear equation have?

A linear equation has exactly one solution, unless a = 0 and b = 0 (infinite solutions) or a = 0 and b ≠ 0 (no solution).

Why are linear equations important?

They model many real-world relationships and are the foundation for more complex mathematical concepts.