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Solving 3 x 3 Linear Systems

Question 2 • OK-Algebra II A

Given that (3, 3, –2) is a solution to the given system, which of the following statements are possibly true of the system?Check all of the boxes that apply.

Answer
A
The three planes represented by the equations in the system are parallel.
B
The system is consistent.
C
The system is inconsistent.
D
The system is independent.

Explanation

Since (3, 3, −2) satisfies all the equations, the system has at least one solution, so it is consistent. It could have exactly one solution, making the system independent; knowing one solution does not rule that out. The planes cannot be parallel, since parallel planes do not all pass through the same point, and the system cannot be inconsistent because it has a solution.

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