11. Find all integers x and y, 0< x, y < n, that satisfy each of the following pairs of congruences. If no x, y exist, explain why not. (a) [BB] 2x + y = 1 (mod n) n = 6 x +3y = 3 (mod n) (b) [BB] x+5y = 3 (mod n) 4x +5y = 1 (mod n) n = 9 (c) x+5y = 3 (mod n) 4x +5y = 1 (mod n) n = 8 (d) 7x + 2y = 3 (mod n) 9x + 4y = 6 (mod n) n = 15 II (e) 3x +5y = 14 (mod n) 5x +9y = 6 (mod n) n = 28

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