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Enhanced Algebra Calculator

Solve linear and quadratic equations with step-by-step explanations and comprehensive algebraic tools

📈 Linear Equations
📊 Quadratic Equations
🔗 System of Equations
📉 Slope Calculator

Linear Equation Solver: ax + b = 0

3x - 15 = 0
x = -b/a
x = 0
Enter coefficients to solve equation

Quadratic Equation Solver: ax² + bx + c = 0

x² - 5x + 6 = 0
x = (-b ± √(b² - 4ac)) / 2a
x₁ = 0, x₂ = 0
Enter coefficients to solve equation

System of Linear Equations (2×2)

Equation 1: a₁x + b₁y = c₁

Equation 2: a₂x + b₂y = c₂

2x + 3y = 8
x - y = 1
Using Cramer's Rule: x = Dₓ/D, y = Dᵧ/D
x = 0, y = 0
Enter coefficients to solve system

Slope Calculator

Point 1 (x₁, y₁)

Point 2 (x₂, y₂)

m = (y₂ - y₁) / (x₂ - x₁)
m = 0
Enter coordinates to calculate slope
📚 Algebraic Fundamentals
📈 Linear Equation Example
3x - 15 = 0
  • Step 1: Add 15 to both sides
  • 3x = 15
  • Step 2: Divide both sides by 3
  • x = 15/3
  • Solution: x = 5
📊 Quadratic Equation Example
x² - 5x + 6 = 0
  • Step 1: Identify a=1, b=-5, c=6
  • Step 2: Calculate discriminant: b² - 4ac = 25 - 24 = 1
  • Step 3: Apply quadratic formula
  • x = (5 ± √1) / 2
  • Solutions: x₁ = 3, x₂ = 2
🔗 System of Equations Example
2x + 3y = 8
x - y = 1
  • Step 1: From equation 2: x = y + 1
  • Step 2: Substitute into equation 1
  • 2(y + 1) + 3y = 8
  • Step 3: Solve: 5y + 2 = 8, so y = 1.2
  • Solutions: x = 2.2, y = 1.2
📉 Slope Example
Points: (1,2) and (5,8)
  • Step 1: Identify coordinates
  • Step 2: Apply slope formula
  • m = (8 - 2) / (5 - 1)
  • m = 6 / 4
  • Slope: m = 1.5
🔑 Key Algebraic Concepts
Variables and Constants
Variables (like x, y) represent unknown values that can change. Constants are fixed numbers that don't change. The goal of algebra is to find the value(s) of the variable(s).
Equation Solving Rules
1. Whatever you do to one side, do to the other
2. Addition and subtraction are inverse operations
3. Multiplication and division are inverse operations
4. Always check your solution by substituting back
Quadratic Formula
For ax² + bx + c = 0:
x = (-b ± √(b² - 4ac)) / 2a

The discriminant (b² - 4ac) tells us:
• Positive: 2 real solutions
• Zero: 1 real solution
• Negative: No real solutions
Slope Interpretation
Slope measures the rate of change:
• Positive slope: line rises left to right
• Negative slope: line falls left to right
• Zero slope: horizontal line
• Undefined slope: vertical line