System of Equations Calculator
Solve systems of linear equations with steps, including substitution-style interpretation and matrix elimination.
Equation Solver
Type any equation. One line for a single equation, multiple lines for a system. Image upload works too.
Your equation
Linear, quadratic, and linear systems are detected automatically. Use x, y, z, w (or x1, x2, ...).
When on, quadratics with a negative discriminant report conjugate complex roots instead of "no real roots".
Result
Solve to see the answer, steps, and precision notes.
How to use the systems calculator
Use the equation solver for two or more linear equations. Enter one equation per line and review the detected variables and solution steps.
- Enter each equation on its own line.
- The solver detects variables and coefficients.
- It applies elimination to find the unique solution when one exists.
Formula or method
A linear system can be represented as Ax = b and solved by elimination.
Worked examples
Two-variable system
Problem: 2x + y = 7 and x - y = 2
Solution: The solution is x = 3, y = 1.
No solution
Problem: x + y = 1 and 2x + 2y = 3
Solution: The lines are parallel/inconsistent, so there is no solution.