Final answer:
When two lines in a system of equations have the same slope and different y-intercepts, they are parallel and do not intersect. Therefore, such a system will always have no solutions, meaning the two equations cannot satisfy the same set of values for x and y simultaneously. Therefore correct option is A
Step-by-step explanation:
The question concerns the graphical representation of a system of equations and whether lines with the same slope will have no solutions. When two lines have the same slope and different y-intercepts, they do not intersect, making them parallel. On a graph, parallel lines never cross each other; therefore, a system of equations represented by parallel lines would not have a point of intersection, meaning there are no solutions to such a system.
If two lines have the exact same slope and the exact same y-intercept, then they are actually the same line and have infinitely many points in common. In the context of the given question which implies that we are considering different equations (and hence different lines), the case of identical lines does not apply, and thus we can affirm that if two lines have the same slope but different y-intercepts, they will never intersect.
So, in response to the question, "The graph of a system of equations with the same slope will have no solutions.", the correct answer is 'Always', assuming that the lines represented by these equations are distinct (different y-intercepts) and thus parallel.