this is not correct
If both 3x and 7y are divisible by 11, then both x and y and any linear combination of the 2 are divisible by 11 yes. HOWEVER, if 3x+7y is divisible by 11 doesn't imply both 3x and 7y are divisible by 11, it means that the sum of their remainders (when each is divided by 11) is divisible by 11. note that (5,1) is in the set of solutions. Neither 5 or 1 is divisible by 11.
The easiest way to do this problem is to take a few point and eliminate. (5,1) eliminates A,C and E. (60,1) eliminates B, so D is our answer. note that (5*12k,1) does the trick was well
Review modulus and congruency classes.