Find the unique solution to the following system of linear e

Find the unique solution to the following system of linear equations: X = [4] in Z_6 X = [10] in Z_15

Solution

X = 4+6t ; t is integer (Using first equation )

Substitute this in second equation :

4+6t = [10] (mod15)

6t = 6 (mod15)

=> t = 1(mod15)

=> t= 1+15s

Substitute t into the formula for x,

x = 4+6(1+15s) = 4+6+90s = 10+90s

So x = 10 (mod 90)