Question

Susi and Janet have been solving systems of equations with one polynomial function of degree two or higher and one linear function. Janet says there must always be one solutions, and Susi says there will always be two solutions. Using complete sentences, explain how Susi can be correct, how Janet can be correct, and how they both can be wrong.

word question

Answer 1

I can explain in pictures.
Susi is correct if the graph's of the functions looks something like this

Answer 2

It'd be easier to visualize what's happening here were we to use actual functions.
Suppose the polynomial function were f(x) = 2x^2 -x + 1 and the linear function were g(x) = -3x + 1. Determine how many solutions there will be to this system.

Answer 3

Janet is correct if the graphs of the functions look something like this

In both drawings I've circled the solutions ( where they intersect)