Question

Given that (3,2,-6) and (-2,5,1) are solutions of two equations in a system of three linear equations, which of the following is true about the system?

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

Answer 1

The system can be either consistent and independent or consistent and dependent.

Step-by-step explanation:

The correct answer is B. The system can be either consistent and independent or consistent and dependent.

In a system of linear equations, the solutions can be classified as consistent or inconsistent and independent or dependent. Consistent means that the system has at least one solution, while inconsistent means that the system has no solution.

In this case, the fact that (3,2,-6) and (-2,5,1) are solutions of two equations means that the system is consistent. However, without more information about the third equation, we cannot determine if the system is dependent or independent. Thus, option B is the most accurate answer.