Answer:
a) neither perpendicular nor parallel
b) perpendicular
Explanation:
a)
3x + 2y = 74
Lets put y in function of x
2y = 74-3x
y = 37 - 1.5 x
On the other hand
9x - 6y = 15
-6y = 15 - 9x
y = -2.5 + 1.5 x
The lines are not parallel because if that is the case, then their slope should be equal, but one slope is 1.5 and the other is -1.5.
If 2 lines are perpendicular, then the product of their slopes should be equal to -1, however 1.5 * -1.5 = -2.25, which is different from -1. Thus, the lines are neither perpendicular nor parallel.
b) 4x - 9y = 8
-9y = 8 - 4x
y = 8/9 +4/9 x
On the other hand
18x+8y = 7
8y = 7 - 18x
y = 7/8 - 9/4 x
The slopes are different, so the lines arent parallel, but they are perpendicular, because
4/9 * (-9/4) = -1