System of Linear Equations Solver interactive tool
Enter system coefficients
x +
y =
x +
y =
Solution
This system has a unique solution:
x1.6667
y2.3333
What Is System of Linear Equations Solver?
A system of linear equations solver finds solutions to 2×2 or 3×3 systems of linear equations. It uses Gaussian elimination to determine whether there is a unique solution, no solution, or infinitely many solutions.
Learning Simultaneous Equations
Students can enter the coefficients of each equation, see when the system is inconsistent, and quickly verify solutions for homework. It reinforces algebra concepts like pivoting, rank, and the relationship between lines or planes in 2D and 3D space.
How To Use the System of Linear Equations Solver
- Choose whether you want to solve a 2x2 or 3x3 system of linear equations from the size dropdown.
- Enter the coefficients for each variable in every equation, followed by the constant term on the right-hand side.
- The system of equations solver will perform Gaussian elimination to reduce the augmented matrix.
- Review whether the system has a unique solution, no solution, or infinitely many solutions based on the output.
- Use the Example button to load a pre-filled system, or Reset to clear all coefficient fields.