Elimination de Gauss

import numpy as np

a=np.array([[7,10],[5,7]],float)
b=np.array([10.1,6.9],float)

n=len(b)
x=np.zeros(n,float)

#forward elimination

for k in range (n-1):
    for i in range (k+1, n):
        facteur=a[i,k]/a[k,k]
        for j in range(k,n):
            a[i,j]=a[i,j]-facteur*a[k,j]
        b[i]=b[i]-facteur*b[k]


#back substitution

x[n-1]=b[n-1]/a[n-1,n-1]

for i in range(n-2, -1, -1):
    sum=b[i]
    for j in range(i+1,n):
        sum=sum-a[i,j]*x[j]
    x[i]=sum/a[i,i]

print("La solution du système est:")
print(x)