Final answer:
The lines represented by the given equations are neither parallel nor perpendicular.
Step-by-step explanation:
To determine the relationship between the lines, we need to compare their slopes.
1. Rewrite the equations in slope-intercept form (y = mx + b):
Equation 1: 15y + 10x = -60
15y = -10x - 60
y = -(2/3)x - 4
Equation 2: y - x = 5
y = x + 5
2. Compare the slopes:
The slope of Equation 1 is -2/3.
The slope of Equation 2 is 1.
3. Analyze the relationship:
Not parallel: Parallel lines have the same slope. These lines have different slopes, so they are not parallel.
Not perpendicular: Perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of -2/3 is 3/2, which is not the slope of Equation 2.
Therefore, the lines are not perpendicular.
Not the same line: The lines have different y-intercepts (-4 and 5), so they cannot be the same line.
Conclusion: The lines represented by the given equations are neither parallel nor perpendicular.