Question

While sitting in class you overheard one of your classmates say, "This equation has infinite solutions, because when I put it in Desmos it gave me parallel lines so I know it makes a conditional equation." Realizing that the student is incorrect, what would you say to help your classmate get their facts straight?

Answer 1

See below

Explanation:

The systems of linear equations represent two lines.

There are 3 possible outcomes with two lines on the plane.

1. Lines intersect

• In this case there is one solution, which is the point of intersection.

2. Lines are parallel

• In this case the lines never intersect, so there is no solution

2. Lines are same

• In this case the lines overlap, so there are infinitely many solutions.