Final answer:
Answer B, y = -8x - 6 and 5y = 4x - 3, is the correct choice because the lines have different slopes and will intersect exactly once, which means they have only one solution.
Step-by-step explanation:
To determine which system of equations has exactly one solution, we need to look for a pair of linear equations that are not parallel and do not coincide, meaning that their slopes are different. A system with exactly one solution will intersect at one point.
- A) y = -8x - 6 and y = -8x + 6: These equations have the same slope but different y-intercepts, so they are parallel and do not intersect. This system has no solution.
- B) y = -8x - 6 and 5y = 4x - 3: When the second equation is simplified to y = (4/5)x - (3/5), we see the slopes are different (-8 and 4/5), so these lines will intersect exactly once. This system has one solution.
- C) y = -8x - 6 and y = 8x - 6: These equations have slopes of equal magnitude but opposite signs, hence they will intersect at one point. This system has one solution.
- D) y = -8x - 6 and y = 8x + 6: Like option C, these lines have slopes of equal magnitude but opposite signs. They will intersect at one point, so this system also has one solution.
However, only option B has distinctly different slopes and does not result in a coincidence of lines (where one line is essentially on top of the other), so the correct answer is B).