Question

What is a quick way to tell other 8 th graders how to tell if an equation will have one solution, no solution, or infinite solutions? Explain how you know and why the equation will have the solution(s) that it doe

Answer 1

see below

Explanation:

We can check the slope and the y intercept.

Assuming these are linear equations

If the slopes are different, they will have 1 point of intersection (one solution)

If the slopes are the same, we need to check the y intercept.

If the y intercept is the same, then the lines are the same and the will have infinite solutions.

If the y intercepts are not the same, the lines are parallel, and they will never intersect and have no solutions.