Answer:
C. a=p, b=q, c≠r
Step-by-step explanation:
The equations will have no solution when they describe lines with the same slope, but different y-intercepts. The slopes of these lines are ...
-a/b and -p/q
One way for -a/b = -p/q is to have a=p and b=q. When that is true, the y-intercepts will be different when c ≠ r.
Choice C offers a condition guaranteeing no solution.
__
Additional comment
Consider the equations ...
2x +3y = 5 4x +6y = 5 . . . note that a≠p, b≠q, c=r . . . matches choice B
These two equations describe parallel lines, so will have no solution. In effect, both choices B and C "may" be true when there is no solution, but neither "must" be true.
