Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?
the system can be either inconsistent or consistent.
the system can be either independent or dependent.
the system can only be independent and consistent.
the system can only be dependent and inconsistent.

A system is said to be consistent if it has at least one solution. A system which has no solution is said to be inconsistent.

A consistent solution is said to be independent if it has only one solution and is said to be dependent if it has an infinitely many solutions.

Given that (1, 0, 1) is a solution to a system of three linear equations, this means that the system is consistent.

But we do not have the information, whether (1, 0, 1) is the only solution, or whether there are other solutions. So it can either be independent or dependent.

Therefore, the correct true statement is that the system can be either independent or dependent.

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