Final answer:
Option D, with the equations 3x + y = 3 and 6x + 2y = 6, represents infinite solutions because one equation is a multiple of the other, showing that they are, in fact, the same line.
Step-by-step explanation:
To determine which pair of equations would result in an infinite number of solutions, they must be equivalent to each other, implying that one can be derived from the other by multiplying or dividing by a constant.
The pair presented as option C:
These cannot have infinite solutions because they are not equivalent; they have the same left-hand side but different constants on the right-hand side, making them parallel lines with no intersection point(s).
The pair presented as option D:
If we multiply the first equation by 2, we get:
which is exactly the same as the second equation. Therefore, option D is the correct answer, as it represents the same line, leading to an infinite number of solutions since any point that lies on one equation's graph will also lie on the other's.