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 solution, 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.

Answer 1

From their statements, they both are wrong in saying that there will always be one solution and there will always be two solutions. Because the answer would depend on the degree of the polynomial function they have. Janet can be right if the function given is linear that is there is only one variable. Susi, on the other hand, can be right if the polynomial has a degree of two or a quadratic equation is given.

Answer 2

Both are incorrect insofar that they say that they use the word always, which certainly is not the case. If the poly has a degree of 2, and a vertex which is for example (0, 5) the line y = x would never intersect it. Y = x + 5 would intersect it at one point, and y = x+10 at two points. The answer also depends on the delta of the function. If delta greater than 0 there will be two solutions, while a delta that is 0 gives one solution. If delta is smaller than 0 we have no solution.