Final answer:
When a system of linear equations has no solution, the lines have different slopes and different intercepts.
Step-by-step explanation:
When a system of linear equations has no solution, it means that the lines represented by the equations do not intersect. In this case, the lines have different slopes and different intercepts. The option that correctly describes the relationship between the lines is B: The lines have the same slope, but different intercepts. If the graph of a system of two linear equations has no solution, this means that the lines are parallel to each other. Parallel lines have the same slope but they never meet, because they have different intercepts. So, given Line A with a slope of -4.7 and Line B with a slope of 12.0, we can conclude that these lines are not parallel and therefore if they were part of a system, it would not be correct to say the system has no solution based on the given slopes. When the slopes of two lines are different, as in this case, it generally means that the lines intersect at a single point and hence, have one solution. For a system to have no solution due to parallel lines, both lines would need to have identical slopes and different y-intercepts.