Linear Equations generator (with solution)

linear_equations_generator.py

#!/usr/bin/python

# Generate 2 linear equations in 2 variables and their solutions
# restrictions: a,b,c,d = positive integeers [1,9]
# matrix:
#| a b || x | = | e |
#| c d || y |   | f |

from fractions import Fraction
from random import randint

howmuch = 10

for i in range(1, howmuch + 1):
    a = randint(1, 9)
    b = randint(1, 9)
    c = randint(1, 9)
    d = randint(1, 9)
    e = randint(-10, randint(0, i))
    f = randint(-10, randint(0, i))

    determinant = a*d - b*c
    no_solution = (determinant == 0)

    print('{}x+{}y={}'.format(a, b, e))
    print('{}x+{}y={}'.format(c, d, f))

    if no_solution:
        print('(no solution)')
        print()
        continue

    sol_x = divmod((e*d - b*f), determinant)
    sol_y = divmod((a*f - e*c), determinant)

    ans_x = Fraction((e*d - b*f), determinant)
    ans_y = Fraction((a*f - e*c), determinant)

    print('({}, {})'.format(str(ans_x), str(ans_y)))
    print()