What is a system of equations?
A system of equations is a group of equations that must be satisfied at the same time. Its solution is the set of variable values that makes every equation true.
Algebra
System of Equations Solver
Solve simultaneous linear equations with two or more variables using elimination, substitution or matrix methods directly in your browser.
Tool
System of Equations Solver
Solve simultaneous linear equations with two or more variables using elimination, substitution or matrix methods directly in your browser.
This tool runs in your browser. Your input is processed locally and is not uploaded.
About this Tool
Enter a set of linear equations to solve all unknown variables together. The solver converts the equations into a consistent system, applies an appropriate method and shows the resulting variable values. It can distinguish between a unique solution, an inconsistent system with no solution and a dependent system with infinitely many solutions. All processing takes place locally in your browser.
Examples
- x + y = 10; x - y = 2
- 2x + 3y = 13; 4x - y = 5
- x + y + z = 6; 2x - y + z = 3; x + 2y - z = 2
- 2x + 4y = 8; x + 2y = 4
- x + y = 3; 2x + 2y = 8
Frequently Asked Questions
How many equations and variables can I enter?
The supported limit depends on the implementation, but the solver is intended for systems with two or more linear equations and variables.
Which solving method does the tool use?
Depending on the system, it may use elimination, substitution or matrix-based row reduction. The selected method and important intermediate steps are shown with the result.
What does a unique solution mean?
A unique solution means there is exactly one set of variable values that satisfies every equation in the system.
Can a system have no solution?
Yes. A system has no solution when its equations contradict one another, such as two parallel lines with different intercepts.
When does a system have infinitely many solutions?
This occurs when one or more equations describe the same relationship and the system does not contain enough independent information to determine one unique solution.
Can the solver handle decimal values and fractions?
Yes. Coefficients and constants may contain supported decimal values or fractions, and exact fractional results should be preserved where possible.
Is the entered system uploaded anywhere?
No. The equations are processed locally in your browser and are not transmitted to a server.