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# Gauss-Crout elimination - solving any systems of equations - calculator

You can calculate any system of linear equations, both homogeneous and heterogeneous with any number of unknowns by Gauss-Crout elimination method. To solve the system of equations using the Gauss-Crout method, enter values by in the text field. the following rule:
- In the first line we enter the number n (number of lines)
- Data from each equation should be entered in separate lines
- The entered coefficients must be separated by at least one space
- The last factor in the line is the factor after the equals sign in equation

eg for a system of equations with five unknowns:

2x1 - 2x2 + 2x3 - 7x4 + 6x5 = -4
7x1 - 3x2 - 2x3 + 7x4 + 2x5 = 11
2x1 + 2x2 - 1x3 + 1x4 + 4x5 = 9
9x1 + 8x2 - 2x3 + 2x4 - 2x5 = 21
4x1 + 8x2 - 3x3 + 3x4 - 1x5 = 16

## Solving systems of equations with the improved Gauss-Crout elimination method

 a1,1x1 + a1,2x2 + a1,3x3 + ... + a1,n-1xn-1 + a1,nxn = b1 a2,1x1 + a2,2x2 + a2,3x3 + ... + a2,n-1xn-1 + a2,nxn = b2 a3,1x1 + a3,2x2 + a3,3x3 + ... + a3,n-1xn-1 + a3,nxn = b3 ... + ... + ... + ... + ... + ... = ... an-1,1x1 + an-1,2x2 + an-1,3x3 + ... + an-1,n-1xn-1 + an-1,nxn = bn-1 an,1x1 + an,2x2 + an,3x3 + ... + an,n-1xn-1 + an,nxn = bn

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