Final answer:
The correct answer is B) b, which represents a system consisting of identical equations y = 3x + 3 and 3x - y = -3, meaning they are the same line and have an infinite number of solutions.
Step-by-step explanation:
To determine which of the given systems of linear equations has an infinite number of solutions, we need to look at the structure of each system. An infinite number of solutions means that the two equations are actually the same line when graphed, leading to them intersecting at every point on the line.
System (a) consists of two separate equations, 3x - 3 = 0 and 5y - 5 = 0. These are two different lines intersecting the axes at different points and are therefore independent of each other. This system does not have an infinite number of solutions.
System (b) consists of the equations y = 3x + 3 and 3x - y = -3. Upon rearranging the second equation, we get y = 3x + 3, which is identical to the first equation. These two equations represent the same line and therefore have an infinite number of solutions.
Therefore, the correct answer is B) b.