Algebra Calculator
Solve linear equations, quadratic equations, simplify expressions, and systems of equations with detailed step-by-step solutions and explanations.
Algebra Calculator
Algebra Help
How to Use the Algebra Calculator
- Select Problem Type: Choose from linear equations, quadratic equations, expression simplification, or systems
- Enter Coefficients: Input the numerical coefficients for your equation type
- View Solution: See the answer along with discriminant information (for quadratics)
- Study Steps: Review the detailed step-by-step solution process
- Verify Results: Check the verification calculations shown in the steps
- Try Examples: Use the reset button to try different coefficient values
Examples and Use Cases
Linear Equations
Quadratic Equations
Understanding the Results
Equation Types
Linear Equations
Form: ax + b = c. Has exactly one solution when a ≠ 0. Graph is a straight line.
Quadratic Equations
Form: ax² + bx + c = 0. Can have 0, 1, or 2 real solutions. Graph is a parabola.
Systems of Equations
Multiple equations with multiple variables. Solution is the point where all equations intersect.
Key Concepts
Discriminant
Δ = b² - 4ac determines the nature of quadratic roots. Δ > 0: two real roots, Δ = 0: one root, Δ < 0: complex roots.
Cramer's Rule
Method for solving systems using determinants. Works when the coefficient matrix is non-singular.
Simplification
Combining like terms to reduce expressions to their simplest form.
Frequently Asked Questions
How do I know if a quadratic equation has real solutions?
Check the discriminant (b² - 4ac). If it's positive, there are two real solutions. If zero, one real solution. If negative, no real solutions (complex roots only).
What does it mean when a system has no solution?
When the determinant equals zero, the system either has no solution (inconsistent) or infinitely many solutions (dependent). The lines are either parallel or coincident.
Can I solve cubic or higher-degree equations?
This calculator focuses on linear and quadratic equations. For cubic and higher-degree polynomials, you would need more advanced numerical methods or symbolic computation tools.
How accurate are the decimal results?
Results are calculated using JavaScript's double-precision arithmetic. Quadratic solutions are rounded to 4 decimal places for readability while maintaining mathematical accuracy.
What if my linear equation has no coefficient for x?
If the coefficient of x is 0, the equation becomes a simple comparison (b = c). It will either always be true (infinite solutions) or never true (no solution).
Can I use this for homework verification?
Yes! The step-by-step solutions show the complete process, making it excellent for learning and verifying your manual calculations. Use it to understand the method, not just get answers.
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