Final answer:
A system of equations with one solution corresponds to the situation where the lines have different slopes, meaning they intersect at a single point. Lines with the same slope but different y-intercepts are parallel and never meet, while lines with both the same slope and y-intercept are coincidental, sharing all points.
Step-by-step explanation:
A system of equations with one solution indicates that the lines represented by these equations intersect at exactly one point. When lines have different slopes, they meet only once since they are not parallel and do not overlap. Therefore, the correct answer is D) The lines have different slopes.
For instance, if line A has a slope of -4.7 and line B has a slope of 12.0, these lines would intersect at one point because their slopes are different. This aligns with the general principle that the slope (m) and y-intercept (b) determine the uniqueness of a line's path, thus affecting the number of solutions when compared with another line.
In summary, B) Incorrect because lines with the same slope and different y-intercepts are parallel and never intersect. C) Incorrect because lines with the same slope and same y-intercepts are in fact the same line, thus have infinitely many solutions since they overlap completely. A) Unable to be determined is too vague without context and does not precisely describe a system with one solution.