find a general solution to the simultaneous congruence equations:

3x congruent to 6 mod 15

2x congruent to 10 mod 12

solving the first, 3x = 15t + 6

i.e. x = 5t + 2

plugging this into the second, 2(5t + 2) congruent to 10 mod 12

i.e. 10t congruent to 6 mod 12

so 10t = 12z + 6

i.e. 5t = 6z + 3

so x = 5t + 2 = 6z + 5

this works for the second, but not the first. What am I doing wrong?