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Chapter 8: Problem 73

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A system of two equations in two variables whose graphs are a circle and a line can have four real ordered-pair solutions.

Short Answer

Expert verified
The statement is false. The correct statement should be: 'A system of two equations in two variables whose graphs are a circle and a line can have at most two real ordered-pair solutions'.

Step by step solution

01

Understanding the problem

In the given statement a system of two equations in two variables whose graphs are a circle and a line can have four real ordered-pair solutions. However, a line can intersect a circle at most at two points. These are the potential solutions of the system.
02

Identifying the error

Since a circle and a line can only intersect at two points at most, they cannot have four real ordered-pair solutions. There might be an error in the understanding of the intersections of a line and a circle.
03

Correcting the statement

Change the given statement to: 'A system of two equations in two variables whose graphs are a circle and a line can have at most two real ordered-pair solutions'.

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