Question

The graph of a system of two linear equations has no solution. What is true about the lines? A. The lines are perpendicular. B. The lines have the same slope, but different intercepts. C. The lines have the same intercept, but different slopes. D. The lines are on top of each other.

Answer 1

Answer:

B. The lines have the same slope, but different intercepts.

Step-by-step explanation:

The solution of a system of linear equations doesn't exist if the lines do not intersect each other at any point. So if there is no solution that means the lines of both equations will not intersect.

Lets look at the options one by one.

For option A:

If the lines are perpendicular, they might intersect at any point so this is not the correct option.

For Option B:

If the lines have same slop and different intercepts that means the lines are parallel. We know that parallel lines never cross each other so option B is the correct answer.

For Option C:

The lines with same intercept and different might also intersect so option C is not correct.

For Option D:

The lines being on top of each other means that the lines intersect on all points. So option D is also not correct.