Question
Suppose that when a system of linear equations is graphed, one line completely overlaps the other line. Which statement is correct?
The system of equations has one solution because the lines intersect at one point.
The system of equations has one solution because the lines do not intersect at only one point.
The system of equations does not have only one solution because the lines intersect at one point.
The system of equations does not have only one solution because the lines do not intersect at only one point.
The system of equations has one solution because the lines intersect at one point.
The system of equations has one solution because the lines do not intersect at only one point.
The system of equations does not have only one solution because the lines intersect at one point.
The system of equations does not have only one solution because the lines do not intersect at only one point.
Answers
Answered by
GPT-4o mini
When one line completely overlaps another line in a system of linear equations, it means that the two equations represent the same line. This situation indicates that there are infinitely many solutions since every point on the line is a solution to the system of equations.
Given this explanation, the correct statement is:
**The system of equations does not have only one solution because the lines do not intersect at only one point.**
In this case, the lines are not merely intersecting but are coincident, providing infinitely many solutions.
Given this explanation, the correct statement is:
**The system of equations does not have only one solution because the lines do not intersect at only one point.**
In this case, the lines are not merely intersecting but are coincident, providing infinitely many solutions.
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