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Algebra Calculator

Solve algebraic equations, systems of equations, and expressions step by step

Equation Type

Select the type of algebraic problem you need to solve

Linear Equation

Solve equations in the form: ax + b = c

Enter coefficients below to see your equation
The number multiplying x
The constant added to ax
The value on the right side of equals

Solution

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Select equation type and enter values
Your algebraic solution will appear here

Step-by-Step Solution

Quick Examples

Linear Equation
2x + 5 = 11
x = 3
Quadratic Equation
x² - 5x + 6 = 0
x = 2, 3
System of Equations
2x + 3y = 7
x - y = 1
x = 2, y = 1
Expression Evaluation
2x + 3y - 5, x=2, y=3
Result = 8
Click any example to load the values and see the solution

Understanding Algebra

Linear Equations

Linear equations have the form ax + b = c, where the variable x appears to the first power only.

Solving Steps

  • Isolate x: Move constants to one side
  • Divide: Divide both sides by the coefficient of x
  • Simplify: Express the answer as a fraction or decimal

Quadratic Equations

Quadratic equations have the form ax² + bx + c = 0, where a ≠ 0.

Quadratic Formula

  • Formula: x = (-b ± √(b² - 4ac)) / 2a
  • Discriminant: b² - 4ac determines number of solutions
  • Positive: Two real solutions
  • Zero: One repeated solution
  • Negative: No real solutions

Systems of Equations

Systems involve multiple equations with multiple variables, solved simultaneously.

Solution Methods

  • Substitution: Solve one equation for a variable, substitute into the other
  • Elimination: Add or subtract equations to eliminate a variable
  • Matrix methods: Using determinants (Cramer's rule)

Types of Solutions

  • Unique solution: One point of intersection
  • No solution: Parallel lines (inconsistent)
  • Infinite solutions: Same line (dependent)

Common Applications

  • Age problems: Finding ages based on relationships
  • Distance problems: Speed, time, and distance calculations
  • Mixture problems: Combining solutions of different concentrations
  • Investment problems: Calculating returns and principal amounts