Final answer:
The given pair of lines is perpendicular.
Step-by-step explanation:
The given pair of lines are:
3 + 7x = 2y
2x + 7y = 5
To determine whether the lines are parallel, perpendicular, or neither, we need to check the slopes of the lines.
The first equation can be rearranged to the form y = mx + b, where m is the slope.
3 + 7x = 2y
2y = 7x + 3
y = (7/2)x + 3/2
From this equation, we can see that the slope of the first line is 7/2.
We can rearrange the second equation to the same form:
2x + 7y = 5
7y = -2x + 5
y = (-2/7)x + 5/7
The slope of the second line is -2/7.
Since the slopes of the lines are not equal, the lines are not parallel.
To determine if the lines are perpendicular, we can check if their slopes are negative reciprocals of each other. The negative reciprocal of (7/2) is -2/7. Since the slopes are negative reciprocals, the lines are perpendicular.