Final answer:
Option a) x+6y= 36 is a correct simplification of 3x + 18y = 108. Options b), c), and d) represent different specific solutions to x and y based on the value of the constants provided.
Step-by-step explanation:
The goal is to determine if each given equation represents a full simplification of the equation 3x + 18y = 108. To do so, we can simplify the original equation by dividing all terms by 3 which results in x + 6y = 36. This matches option a), verifying that it is indeed simplified correctly. Next, options b), c), and d) introduce different constants on the right side of the equation, indicating different solutions based on the value of x and y. Option d) is an equivalent equation to the original one, as multiplying both sides by 3 again would result in the initial equation given.