Final answer:
The system of equations has an infinite number of solutions since both equations represent the same line when simplified.
Step-by-step explanation:
The student's question involves solving a system of linear equations, which can be addressed by using algebraic methods such as substitution or elimination. Given two equations, -3x + 5y = 2 and 9x - 15y = 6, we must determine the type of solutions they represent when graphed. Since both equations represent lines, we are looking for their point(s) of intersection. To solve for the solutions, we multiply the first equation by 3 to get -9x + 15y = 6, which is identical to the second equation when simplified, indicating that the two lines are the same. Therefore, the system does not have a unique solution but rather an infinite number of solutions, which can be described by rearranging the first equation to solve for x in terms of y:
x = (5/3)y + (2/3).
So, the correct answer is B) infinite solutions of the form (5/3 y+2/3, y).