Question

Given a system of linear equations in three​ variables, which of the following statements is not ​true?

Choose the incorrect statement below.

A.

If the system is​ consistent, then the system could have no solutions.

B.

If the system is​ consistent, then the system could have one unique solution.

C.

If the system is​ consistent, then the system could have infinitely many solutions.

D.

If the system is​ inconsistent, then the system has no solution

Answer 1

Answer: Choice A

"If the system is​ consistent, then the system could have no solutions" is the false statement.

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Step-by-step explanation:

Let's go through the answer choices to see which are true and which are false.

• A. This is false. The reason being is that a consistent system always has at least one solution (see choices B and C). Inconsistent systems on the other have no solutions.
• B. This is true. A consistent system has one or more solutions.
• C. This is true for similar reasons as choice B.
• D. This is true. An inconsistent system has no solutions.

So to recap:

• consistent ---> one or more solutions
• inconsistent ---> no solutions