Chinese Remainder Theorem: Divisibility in Arithmetic

[mtayab1994]

Chinese remainder theorem help

Homework Statement

Solve in $$Z^{2}:6x-5y=1$$

Conclude the solution to the system:

X≡2(mod5) , X≡1(mod6)

The Attempt at a Solution

1- solved the equation and found one unique solution which was S={(1,1)}

Given:
X≡2(mod5) , X≡1(mod6)

X≡2(mod5) means X=5t+2

X≡1(mod6) means 5t+2=1(mod6) which is 5t=-1(mod6) But how can i proceed from here on?

 

[mtayab1994]

Solved it :)