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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

Mastering Algebra

What is Algebra?

Algebra is the branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations. Think of it as arithmetic with mystery numbers - you're solving puzzles to find what those mystery values are.

Linear Equations Explained

  • Standard form: ax + b = c (where x is raised to power 1)
  • One solution: Every linear equation has exactly one answer
  • Real-world use: Distance = speed × time problems
  • Solving method: Isolate x by undoing operations

Quadratic Equations Mastery

  • Standard form: ax² + bx + c = 0 (x is squared)
  • Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
  • Discriminant magic: b² - 4ac tells you solution count
  • Two solutions: Most quadratics have two x-values

Systems of Equations Strategy

Systems are multiple equations working together - like having multiple clues in a detective story. You need all the clues to solve the mystery of finding x and y values that satisfy everything.

Solution Methods That Work

  • Substitution: Solve one equation, plug into the other
  • Elimination: Add/subtract equations to cancel variables
  • Graphing: Find where two lines intersect
  • Matrix method: Use determinants (Cramer's rule)

Real-World Applications

  • Business: Break-even points and profit calculations
  • Physics: Motion equations and projectile paths
  • Economics: Supply and demand intersections
  • Engineering: Load calculations and design constraints

Common Problem Types

  • Age problems: "Mary is twice as old as John..."
  • Mixture problems: Combining different concentrations
  • Work rate problems: Two people working together
  • Investment problems: Different interest rates