To find:The given statement is true or false. If false replace underlined term to make true sentence.
Answer to Problem 3SGR
The given statement is false.
The true statement is: If a consistent system has an infinite number of solution(s), it is said to be consistent.
Explanation of Solution
Given information:
The given statement:
If a consistent system has an infinite number of solution(s), it is said to be inconsistent.
Concept used:
If a system has at least one solution, then it is said to be consistent. If a consistent system of equations has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it isdependent,when graphed such equations, represent the same line. If a system has no solution, it is said to be inconsistent .The graphs of such equations do not intersect, i.e., graphs are parallel.
If there exist at least one solution of a system of equations then system is called consistent.
Hence, the given statement is false.
The true statement out of the given statement is:
If a consistent system has an infinite number of solution(s), it is said to be consistent.
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