Problem 2. Find all integer solutions to the equation 9x + 15y = 12. Problem 3. Find all the solutions of each of the following linear congruences. (a) 9x = 12 (mod 15) (b) 17x = 14 (mod 21) (d) 7x = 1 (mod 31) (c) 15x = 9 (mod 25) (e) 7x = 22 (mod 31) (You can solve this in the same manner as the previous four. Or, you can find a way to use part (d) for a quicker solution.) Problem 4. Find all solutions of each of the following systems of linear congruences 2x = 1 (mod 5) 3x = 9 (mod 6) 4x = 1 (mod 7) 5x = 9 (mod 11) x = 1 (mod 3) (a) x = 2 (mod 5) x = 3 (mod 7) x = 5 (mod 11) (b) x = 14 (mod 29) x = 15 (mod 31) (c)