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Determine whether the statement is true or false.
For a system of two linear equations in two variables, if the graphs of the equations are parallel lines, then the system of equations has infinitely many solutions. [6.1]
![Check Mark](/static/check-mark.png)
Whether the given statement is true or false.
Answer to Problem 1MC
The given statement is false.
Explanation of Solution
Given:
The given statement is “For a system of two linear equations in two variables, if the graphs of the equations are parallel lines, then the system of equations has infinitely many solutions”.
Calculation:
The number of solutions of a system of equations in two variables can be determined based on the nature of the graphs of the equations as follows.
- If the graphs of the equations in a system that involves two equations with two variables are intersecting, then the system has a unique solution.
- If the graphs of the equations are parallel, then the system has no solution.
- If the system has infinitely many solutions, then the graphs of the two equations with two variables are coinciding with each other.
Thus, it is not possible for the system to have infinitely many solutions if the graphs of the equations are parallel.
Therefore, the statement is false.
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Chapter 6 Solutions
College Algebra: Graphs and Models (6th Edition)
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