To find the values of x and y using Euclid's division algorithm, we need to find the greatest common divisor (GCD) of 15 and 12.

Using Euclid's division algorithm:

Step 1: Divide 15 by 12.

15 = 12 * 1 + 3

Step 2: Divide the previous divisor (12) by the remainder (3).

12 = 3 * 4 + 0

Since the remainder is now 0, we stop the algorithm. The GCD of 15 and 12 is the last non-zero remainder, which is 3.

Now, we can express the GCD (3) as a linear combination of 15 and 12:

3 = 15 - 12 * 1

Therefore, the values of x and y are:

x = -1

y = 1