Equation Solver
Solve equations step-by-step with detailed explanations. Supports linear, quadratic, polynomial, exponential, logarithmic, and systems of equations.
Equation Solving Methods
Equations are mathematical statements that assert the equality of two expressions. Solving equations means finding the values of variables that make the equation true.
Linear Equations
Linear equations have exactly one solution (unless they're inconsistent or have infinitely many solutions).
Quadratic Equations
- $\Delta > 0$: Two real solutions
- $\Delta = 0$: One real solution
- $\Delta < 0$: Two complex solutions
Solving Methods
| Method | Best For |
|---|---|
| Factoring | Quadratics that factor nicely |
| Quadratic Formula | Any quadratic equation |
| Completing the Square | Converting to vertex form |
| Substitution | Systems of equations |
| Elimination | Linear systems |
| Gaussian Elimination | Large systems, matrices |
Systems of Equations
A system of equations is a collection of equations with the same variables. Solutions are values that satisfy all equations simultaneously.
$ax + by = e$
$cx + dy = f$
where $D = ad - bc$ (determinant)
Solving Tip:
Always check your solutions by substituting them back into the original equation. This helps catch calculation errors and verify that your answer is correct.
Common Equation Types
Equation Solver Answers
What does the equation solver do?
The equation solver finds the solution(s) to mathematical equations, whether linear, quadratic, or more complex. It helps determine the value(s) of the variable(s) that satisfy the equation.
What types of equations can it solve?
It can solve linear equations, quadratic equations, systems of equations, and even some polynomial or exponential equations depending on the complexity and input format.
Does it show step-by-step solutions?
Yes, many equation solvers provide detailed steps to help users understand how the solution is found, which is especially helpful for students learning algebra or calculus.
Can it solve equations with multiple variables?
Yes. For systems of equations with multiple variables, the solver can find simultaneous solutions using methods like substitution, elimination, or matrix techniques.