Two shipping plans are described by y = 5x + 20 and y = 5x + 35, where x is the number of packages and y is the total cost. How many…

Both equations have slope $5$ but different $y$-intercepts, $20$ and $35$. Lines with the same slope and different intercepts are parallel and never intersect, so the system has no solution, choice A. Algebraically, setting them equal gives $5x+20=5x+35$, which simplifies to $20=35$, a false statement. Choice D (infinitely many) would happen if the intercepts were also equal. Choice B (one solution) requires different slopes. Choice C is impossible for two lines, which cross at most once unless they coincide.