Final answer:
The system has one solution and the solution is the intersection of the two lines.
Step-by-step explanation:
In order to determine which statements about the system of linear equations are true, we need to analyze the equations.
First, we can rewrite both equations in slope-intercept form (y = mx + b) to determine the slope and y-intercept.
Equation 1: 2y = x + 50 -> y = (1/2)x + 25
Equation 2: 3y = 3x + 15 -> y = x + 5
a) The system has one solution: This statement is true because the two lines have different slopes (1/2 and 1) and different y-intercepts (25 and 5), so they will intersect at a single point.
b) The system graphs parallel lines: This statement is false because the slopes of the two lines are different.
c) Both lines have the same slope: This statement is false because the slopes of the two lines are different.
d) Both lines have the same y-intercept: This statement is false because the y-intercepts of the two lines are different.
e) The equations graph the same line: This statement is false because the slopes and y-intercepts of the two lines are different.
f) The solution is the intersection of the two lines: This statement is true because the solution to the system of equations is the point where the two lines intersect.