Chapter 7.1, Problem 63E

Solution

To choose: The incorrect option from the following options.

A. 1

B. 2

C. 4

D. 5

E. infinitely many

The incorrect option is (D).

Given Information:

The statement is “The number of solutions of a system of two equations in two variables whose graphs are parabolas.”

Explanation:

Consider the given information,

Try to imagine all possible systems consisting of a parabola and a parabola, and the respective possible points of intersection.

As shown in the graph, the circle is kept in a fixed position as the parabola moves, indicating the possible circle−parabola configuration within the system.

  

So there is one solution, so the option (A) is correct.

And,

  

So there is 2 solution, so the option (B) is correct.

And,

  

So there is 4 solution.

And,

  

So there is 4 solution, so the option (C) is correct.

And,

  

So there are infinite many solution, so the option (E) is correct.

Thus, there is no condition, which is showing 3 solution.

Therefore, the required option is (D).