Q1.find an inverse of 19modulo 43.

so far I have worked through euclids algorithm to find gcd(19,43)=1. however when I try to work the algorithm in reverse to solve 19x +43y=1 I get confused.

Q2. Solve 19x congruend to 17 mod 43.

I assume this will be easier to answer once I have the answer for q1?! I have attempted to solve this by trying to solve 19x-43t=17, again I have worked through euclids algorithm to find again that gcd(19,43)=1, however once again I get confused when trying to work the algorithm in reverse.

Q3. Solve the system 19x congruent to 17 mod 43 and

x congruent to 18 mod 19.

Again I assume this will be easier once I have solved q1 and 2.