9
QuizMultiple Choice

Modeling with Linear Systems

Question 9 • OK-Algebra II A

Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?

Answer
A
The system can be either inconsistent or consistent.
B
The system can be either independent or dependent.
C
The system can only be independent and consistent.
D
The system can only be dependent and inconsistent.

Explanation

Because (1, 0, 1) is a solution, all three equations are satisfied by that same ordered triple, so the system is consistent. A consistent system may have exactly one solution (independent) or infinitely many solutions (dependent). Therefore, it can be either independent or dependent.

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