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
Calculation Examples
Linear Equations
Quadratic Equations
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.
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.
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