Final answer:
Option B, which contains the system of linear equations 5x - 5y = -9 and 15x - 15y = -27, has an infinite number of solutions because the second equation is a multiple of the first, indicating they are equivalent.
Step-by-step explanation:
To determine which system of linear equations has an infinite number of solutions, we can look for pairs of equations that are multiples of each other. An infinite number of solutions means that the equations are equivalent, representing the same line in a graph.
System A: 3x + 5y = 10; 2x + 3y = 6
System B: 5x - 5y = -9; 15x - 15y = -27
System C: 5x - 5y = -9; 15x - 15y = -20
System D: 5x - 5y = -9; -x - 5y = -6
Upon inspection, System B is the only one where the second equation is a multiple of the first. If you multiply the first equation by 3, you'll get the second equation:
3(5x - 5y) = 3(-9)
15x - 15y = -27
Since both equations in System B represent the same line, the answer is Option B.