Equation Solver
Solve linear equations, quadratic equations, and systems of linear equations with step-by-step solutions. Perfect for students, teachers, and professionals who need accurate algebra solutions.
What Is an Equation Solver?
An equation solver is a tool that finds the value(s) of variables that satisfy a given equation. This calculator can solve three types of equations:
- Linear Equations: ax + b = 0 — one variable, one solution.
- Quadratic Equations: ax² + bx + c = 0 — up to two real or complex solutions.
- Systems of Linear Equations: Two equations with two variables, one unique solution.
How Does the Equation Solver Work?
The calculator uses standard algebraic methods:
Linear Equations: Isolate the variable by adding, subtracting, multiplying, or dividing both sides.
Quadratic Equations: Uses the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
Systems of Equations: Uses substitution, elimination, or Cramer's rule.
Step-by-step solutions are displayed to help you understand the process.
Why Use This Equation Solver?
- Three Solver Types: Linear, quadratic, and systems of equations.
- Step-by-Step Solutions: Learn the solving process.
- Graph Visualization: See equations plotted on a graph.
- Free & Private: No registration, no data storage.
- Mobile-Friendly: Works on any device.
❓ Equation Solver FAQ
What types of equations can this solver handle?
This solver can handle linear equations (ax + b = 0), quadratic equations (ax² + bx + c = 0), and systems of two linear equations (ax + by = c, dx + ey = f).
What is a linear equation?
A linear equation is an equation of the form ax + b = 0, where a and b are constants and x is the variable. It has one solution: x = -b/a.
What is a quadratic equation?
A quadratic equation is of the form ax² + bx + c = 0, where a ≠ 0. It can have two real roots, one real root, or two complex roots depending on the discriminant.
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a. It gives the solutions to any quadratic equation.
What is the discriminant?
The discriminant is b² - 4ac. If it's positive, there are two real roots. If it's zero, there is one real root. If it's negative, there are two complex roots.
What is a system of equations?
A system of equations is a set of two or more equations with the same variables. This solver handles systems of two linear equations with two variables.
How does the solver handle systems of equations?
It uses Cramer's rule, which solves for each variable using determinants. For the system ax + by = c and dx + ey = f, x = (ce - bf)/(ae - bd) and y = (af - cd)/(ae - bd).
What if the system has no solution?
If the equations are parallel (a/d = b/e ≠ c/f), there is no solution. The calculator will indicate this in the results.
What if the system has infinite solutions?
If the equations are the same line (a/d = b/e = c/f), there are infinite solutions. The calculator will indicate this.
How do I enter a linear equation?
Enter the coefficients a and b in the linear equation mode. The equation is ax + b = 0. For example, to solve 2x - 6 = 0, enter a = 2 and b = -6.
How do I enter a quadratic equation?
Enter the coefficients a, b, and c in the quadratic equation mode. The equation is ax² + bx + c = 0. For example, to solve x² - 5x + 6 = 0, enter a = 1, b = -5, c = 6.
How do I enter a system of equations?
Enter the coefficients for each equation in the system mode. For example, to solve 2x + 3y = 8 and 3x - 2y = 1, enter a₁=2, b₁=3, c₁=8, a₂=3, b₂=-2, c₂=1.
What is the difference between a linear and a quadratic equation?
A linear equation has the highest power of 1 (x¹). A quadratic equation has the highest power of 2 (x²). Linear equations have one solution, while quadratic equations can have up to two solutions.
What is Cramer's rule?
Cramer's rule is a method for solving systems of linear equations using determinants. For a 2x2 system, x = (ce - bf)/(ae - bd) and y = (af - cd)/(ae - bd).
Can this solver handle complex roots?
Yes. For quadratic equations with a negative discriminant, the solver will display the complex roots in the form a ± bi.
How accurate is this equation solver?
This solver uses standard algebraic formulas and provides accurate results. Decimal precision can be adjusted in the advanced options.
Can I use this calculator for homework?
Yes! This calculator is designed to help students learn algebra by showing step-by-step solutions. It's a great tool for checking your work and understanding the solving process.