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Algebra Equation Solver

Solve linear and quadratic equations with step-by-step solutions. Perfect for WAEC, KCSE, Matric, and university mathematics preparation.

LinearQuadraticStep-by-Step
Equation Solver
Linear (ax + b = c)
Quadratic (ax² + bx + c = 0)
Simultaneous

Enter coefficients for: ax + b = c

Formulas

Linear: ax + b = c
Solution: x = (c - b) / a

Quadratic: ax² + bx + c = 0
x = (-b ± √(b²-4ac)) / 2a
Discriminant: D = b²-4ac

Simultaneous: Cramer's Rule
D = a₁b₂ - a₂b₁
x = (c₁b₂ - c₂b₁) / D
y = (a₁c₂ - a₂c₁) / D

Exam Tips

  • WAEC: Quadratics appear in Paper 1 & 2
  • KCSE: Simultaneous equations in Paper 2
  • Matric: All types in Paper 1
  • Always check by substituting back
  • Show all working for full marks

Algebra Equation Solver for African Students

Algebra is a fundamental branch of mathematics that forms the backbone of secondary and tertiary education curricula across Africa. Whether you're preparing for WAEC (West African Examinations Council), KCSE (Kenya Certificate of Secondary Education), South African Matric examinations, or university entrance tests, strong algebra skills are essential.

This equation solver handles three common types: linear equations (ax + b = c), quadratic equations (ax² + bx + c = 0), and simultaneous linear equations (two equations with two unknowns). Each solution includes detailed step-by-step working, helping you understand the process rather than just getting the answer.

For quadratic equations, the solver uses the quadratic formula (also known as the "almighty formula" in Nigerian math classes): x = (-b ± √(b²-4ac)) / 2a. It calculates the discriminant to determine whether the equation has two real roots, one repeated root, or complex roots. Understanding the discriminant is crucial for exam success.

Simultaneous equations are solved using Cramer's Rule (determinant method), which is efficient and systematic. This method is particularly useful in exams where you need to show clear, organized working. The solver also verifies the solution by substituting back into both original equations.

Frequently Asked Questions

What is the quadratic formula?

The quadratic formula is x = (-b ± √(b²-4ac)) / 2a, used to solve equations of the form ax² + bx + c = 0. The expression b²-4ac under the square root is called the discriminant. If it's positive, there are two real solutions; if zero, one repeated solution; if negative, no real solutions (complex roots).

How do I solve simultaneous equations?

There are three main methods: substitution (solve one equation for a variable, substitute into the other), elimination (add/subtract equations to cancel a variable), and Cramer's Rule (using determinants). This solver uses Cramer's Rule, which is systematic and works well for 2x2 systems.