Algebra Calculator
Solve linear equations, quadratic equations, and systems of equations with step-by-step solutions and detailed explanations.
Calculator
Enter your information to calculate results
Linear Equation: ax + b = 0
Enter the coefficients a and b to solve for x
Equation: 2x + (6) = 0
How It Works
The algebra calculator solves different types of equations using standard algebraic methods:
Linear Equations (ax + b = 0):
x = -b/a
Quadratic Equations (ax² + bx + c = 0):
x = (-b ± √(b² - 4ac)) / (2a)
System of Equations:
Uses Cramer's rule with determinants to find unique solutions
Examples
Linear Example
Equation: 2x + 6 = 0
Solution: x = -3
Quadratic Example
Equation: x² - 5x + 6 = 0
Solutions: x = 2, x = 3
System Example
Equations:
2x + 3y = 7
x - y = 1
Solution: x = 2, y = 1
Compare
Types of Solutions:
- Linear: One solution, no solution, or infinite solutions
- Quadratic: Two real solutions, one repeated solution, or complex solutions
- System: Unique solution, no solution, or infinite solutions
Applications:
- Physics: Motion equations, force calculations
- Economics: Supply and demand intersections
- Engineering: Circuit analysis, structural calculations
- Optimization: Finding maximum and minimum values
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