Algebra
System of Equations Solver
Solve simultaneous linear equations by entering the augmented matrix and applying Gauss–Jordan elimination.
linear systemgaussian eliminationaugmented matrix
Linear System Solver
Enter an augmented matrix (coefficients | constants) to solve Ax = b.
x1
2
x2
1
Gauss–Jordan reduction
Row operations transform the augmented matrix [A | b] into reduced row-echelon form, revealing the solution vector x.
How to use
- Enter each equation as a row of coefficients with the constant term last.
- Ensure every row has the same number of entries.
- Review the solved variables instantly or adjust the system if it’s singular.
Example
Input: 2 1 5\n1 −1 1
Output: x₁ = 2, x₂ = 1
FAQ & notes
Can it detect infinite solutions?
If the system lacks a unique solution the solver flags the input so you can inspect the equations manually.
How many variables can it solve?
Use up to six variables comfortably. Larger matrices may amplify floating-point error.