a)
To explain: The system has many solutions.
a)
Answer to Problem 31E
The statement is never true.
Explanation of Solution
Given information: The linear equations are
Since two lines can never be the same line for any values of
Hence, the given statement is never true.
b)
To explain: The system has no solution.
b)
Answer to Problem 31E
The statement is sometimes true.
Explanation of Solution
Given information: The linear equations are
Since two lines can no solution if they have the same slope or parallel.
Hence, the given statement is sometimes true.
c)
To explain: If
c)
Answer to Problem 31E
The statement is always true.
Explanation of Solution
Given information: The linear equations are
Since two lines have distinct slopes and will intersect at only one point.
Hence, the given statement is always true.
Chapter 5 Solutions
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