Question

How many solutions does a system of two linear equations have if the slope of each equation is the same, but the y-intercepts are different?

A. infinitely many
B. none
C. one
D. none of the above

Answer 1

The correct answer is b. none

Explanation:

The lines being described are parallel. Parallel lines have the same slope, but different y-intercepts. By definition, parallel lines do not intersect and therefore do not create a solution within a system.

Answer 2

B.) none

Explanation:

In this case a solution means that these lines will intersect at some (x,y) point. If the y-intercept is different but the slope is the same this means that the lines are never going to touch since they will be going up/down at the same rate. This also means that both lines are parallel to one another, since the lines will never touch there will be no solutions.