What makes a system inconsistent or consistent? Dependent or independent?
For example I just graphed a system and it came out to be two parallel lines, I think that this means it's inconsistent and independent, and I believe that's right, but I'm not sure because I am unsure of the definitions.

Question

What makes a system inconsistent or consistent? Dependent or independent?
For example I just graphed a system and it came out to be two parallel lines, I think that this means it's inconsistent and independent, and I believe that's right, but I'm not sure because I am unsure of the definitions.

anonymous · Answer

@whpalmer4 
@Vandreigan

anonymous · Answer

Hmm, I'll need to look up the terms to refresh my memory. Not terms that I use often. One moment :)

anonymous · Answer

So, consistent means that there is at least one solution to the system of equations. Inconsistent means there are no solutions. So for parallel lines, you'd be correct: they are inconsistent.

anonymous · Answer

Alrighty, and independent or dependent?

anonymous · Answer

Independent means there is exactly ONE solution (at least for linear equations). Dependent means there are infinitely many solutions (both lines are exactly the same).

anonymous · Answer

So what is a system of parallel lines

anonymous · Answer

Inconsistent. From what I'm reading, you can only talk about "independent vs dependent" if the system is consistent. http://www.algebra.com/algebra/homework/coordinate/Types-of-systems-inconsistent-dependent-independent.lesson

anonymous · Answer

Just confirmed with another source. Independent and dependent both imply that the system is consistent. That is to say, both terms mean that there is at least one answer, so they'll never be paired with inconsistent.

If a system is inconsistent, that's it. It's just inconsistent.

anonymous · Answer

Alright, I didn't see that there was a just inconsistent choice. Thanks a bunch once more

anonymous · Answer

So, to summarize:

Inconsistent: No solution. Lines are parallel, but not the same line.
Consistent: One or more solutions. Lines intersect, or are the same line.
   -Dependent: Infinitely many answers. Both lines are actually the same line.
   -Independent: Only one answer. Lines are not the same, but intersect (have different slopes)

anonymous · Answer

There isn't a choice for just inconsistent?

anonymous · Answer

There is, I just hadn't noticed before so I was confused

anonymous · Answer

Oh, haha :)