Use the method given in the proof of the Chinese Remainder Theorem (Theorem 11.8) to solve the linear modular system {x = 5 (mod 9), x = 1 (mod 11)}. Theorem 11.8. (Chinese Remainder Theorem) Let m, n E N with gcd(m, n) = 1, and let a, b E Z. Then the system of linear modular equations {x = a (mod m), x = b (mod n)} has exactly one solution in [0, mn).