Aline passes through each pair of points. determine if the system has no solution, one solution, or an infinite number of solutions. (4,1) and (0,1) (0,-4) and (4,4)

Let's take each pair of points and find the slope of the line that connects them.

For each pair of points let's call the first one and the second .

We then substitute into the formula for the slope which is:


FIRST PAIR OF POINTS


SECOND PAIR OF POINTS


If two line have the same slope they are parallel and do not meet. These have different slopes so they are not parallel and will intersect at a point. That point gives the one solution to the system.

The system has one solution.