Systems of Equations Calculator

Solve systems of linear equations using Gaussian elimination with partial pivoting.

Number of Equations

Enter Coefficients

xyz=

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