Solve the following equations for x and y or show that no solution exists. Show your work (in particular,what division must you carry out to solve each case).
(i) 5x + 23 6 mod 47
(ii) 9x + 80 2 mod 81
(iii) The system of simultaneous equations
30x + 3y 0 mod 37 and y 4 + 13x mod 37