Question

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.

Answer 1

@Directrix, @dtan5457

Answer 2

I am thinking that "Given that (1, 0, 1) is a solution to a system" could mean that the point is the only solution or it could be one of many solutions to the system.

Answer 3

I think so, but I couldn't figure it out for sure.

Answer 4

NO solution : inconsistent
1 or more solutions : consistent

Unique solution : Independent

(1,0,1)
this can be unique solution or one of the infinitely many solutions.

Answer 5

The possibilities for a system of two equations are the same as the possibilities for 3 equations, I wonder.

Answer 6

I'm thinking that this scenario could be like options A and C on the attachment but not like option B which is no solution.

Answer 7

I have always found the consistent, inconsistent classification to be confusing.

Answer 8

That is why I keep a chart.

Answer 9

So, what do you think the answer is ?

Answer 10

If it helps, I've been using this to figure out how to classify a system.

Answer 11

No solution = Inconsistent
All other cases : Consistent

Answer 12

Infinetely many : dependent
All other case : Independent

Answer 13

I'm thinking C.

Answer 14

nopes :P

Answer 15

What about this: three lines which coincide at every point. (1, 0, 1) is one of infinitely many solutions?

Answer 16

They lie atop each other. They are the same line.