Solve the following equations for a and b or show that no solution exists. Be sure to show all steps of your work, including any calls to the ged or extended-gcd algorithms. (a) 5a + 23 = 6 mod 499 (b) 9a 80 2 mod 81 (c) 30a + 3b-0 mod 37, and simultaneously -4+ 13a mod 37 Solve the following equations for a and b or show that no solution exists. Be sure to show all steps of your work, including any calls to the ged or extended-gcd algorithms. (a) 5a + 23 = 6 mod 499 (b) 9a 80 2 mod 81 (c) 30a + 3b-0 mod 37, and simultaneously -4+ 13a mod 37