Final answer:
Without complete certainty regarding Option D due to a potential typo, we cannot definitively identify which system of equations has no solution. For the other options, all contain slopes that are not equal, hence, none of these options are systems of parallel lines which would indicate no solution.
Step-by-step explanation:
To determine which system of linear equations has no solution, we can analyze their slopes and y-intercepts. A system of equations has no solution when the lines are parallel, meaning they have the same slope but different y-intercepts.
- Option A: The slopes are -4 and 2, which are not equal, so the lines are not parallel.
- Option B: The slopes are 4 and 2, which are not equal, so the lines are not parallel.
- Option C: The slopes are -4 and 2, which again, are not equal, so the lines are not parallel.
- Option D: The equation y = -4-x is likely a typo. If it should be y = -4x, then the slopes are -4 and 2, which are not equal. However, if the equation is correctly read as y = -4−x (-4 minus x), then the line is horizontal and therefore cannot be parallel to any line with a nonzero slope.
Without knowing for certain if Option D is a typo or not, we cannot definitely identify which system has no solution, but if Option D is meant to be y = -4 - x, it is not possible for it to be the system with no solution as it is a horizontal line and not parallel to any line with a nonzero slope. If the system in Option D is corrected and stated as y = -4x and y = 2x - 3, then it would also not have any solution as the lines are not parallel (slopes are -4 and 2).