Systems of Equations Calculator
Solve systems of linear equations using Gaussian elimination with partial pivoting.
Number of Equations
Enter Coefficients
| x | y | z | = |
|---|---|---|---|
Equations
2x + 1y - 1z = 8
3x - 1y + 2z = -11
2x + 1y + 2z = -3
Solution
x = 2.000000
y = 3.000000
z = -1.000000
Verification
Equation 1 residual0.0000e+0
Equation 2 residual0.0000e+0
Equation 3 residual8.8818e-16
Row Echelon Form
-3.000
-1.000
2.000
-11.000
0.000
1.667
0.667
4.333
0.000
0.000
0.200
-0.200
Method: Gaussian Elimination
- 1. Form augmented matrix [A|b]
- 2. Apply partial pivoting for stability
- 3. Forward elimination to row echelon form
- 4. Back substitution to find solution