def gauss(A,b,offset=(0,0)):
    ox,oy = offset
    if len(A)-1 < oy:
        return A,b

    for i in range(oy,len(A)):
        if A[i][ox] != 0:
            if i > oy:
                A[i], A[oy] = A[oy], A[i]
                b[i], b[oy] = b[oy], b[i]
            break

    for i in range(oy+1,len(A)):
        if A[i][ox] != 0:
            c = A[i][0]/A[oy][0]
            A[i] = [ (A[i][x] - A[oy][x]*c) for x in range(ox,len(A[i])) ]
            b[i] = b[i] - b[oy]*c

    return gauss(A,b,offset=(ox+1,oy+1))


def vprint(A):
    for i in range(len(A)):
        print("%3d" % A[i])

def pprint(A):
    for i in range(len(A)):
        print( " ".join(["%3d" % (A[i][j]) for j in range(len(A[i])) ]) )


A = [ [ 1, 1 ],
      [ 1,-1 ] ]

b = [ 5,
      3 ]

pprint(A)
vprint(b)


A, b = gauss(A,b)

pprint(A)
vprint(b)