Problem 73
Question
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.
Step-by-Step Solution
Verified Answer
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'.
1Step 1: 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.
2Step 2: 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.
3Step 3: 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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