Which is not a possible solution of a system of linear equations?
A.
no solution
B.
only one point
C.
only two points
D.
infinitely many solutions

Question

Which is not a possible solution of a system of linear equations?
A.
no solution
B.
only one point
C.
only two points
D.
infinitely many solutions

e.mccormick · Answer

Know what the linear part of linear equations means?

anonymous · Answer

I want to say B. But I'm not 100% sure.

e.mccormick · Answer

Linear ... line-ar... lines.

How many places can lines intersect?  There are three ways lines can exist in relation to each other.

anonymous · Answer

what do u mean three ways they can exist are u meaning parallel, perpendicular lines and such or something different.

e.mccormick · Answer

Parallel is one in planes.  Perpendicular is not really part of this concept.

What is special about parallel lines that is in the answer choices?

anonymous · Answer

infinitely many solutions  i don't really know though.

e.mccormick · Answer

No, that would be if they were the same line.

e.mccormick · Answer

The plane (two dimensions) is the simplest form of linear equations, so it is good to work there, but the basic rules apply no matter how many dimensions you are in.

You can have the same line twice.
You can have two lines that never touch.
You can have two lines that cross.

anonymous · Answer

wait parallel never intersect so that would be no solution.

e.mccormick · Answer

Yes.  So no solution is NOT the answer because it is possible.

anonymous · Answer

ok and infinitely many solutions the lines overlap so that is possible too.

e.mccormick · Answer

Yep.  That gets rid of A and D.  So, what about 1 or 2 points?

anonymous · Answer

i am not sure what that means but i don't ever see a graphed line containing only one point.

e.mccormick · Answer

Which ones are line graphs:
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e.mccormick · Answer

A linear system means more than one line.  They may share the same space, but there is more than one line.

anonymous · Answer

a linear system of equations can have no solution, a unique solution, or infinitely many solutions so the answer is C.

anonymous · Answer

ok thank-you everybody. i while @jimmyntare gave me the answer i am going to have to give the best answer to @e.mccormick  for explaining it to me so well now i understand it for myself now.

e.mccormick · Answer

Yah, that was why I was trying to get you to think about lines.  When you can see them, it can be easier to remember them because 70% of sensory processing is visual.  Visualization is powerful.

As long as you can see in your mind's eye that only a curve and a line can intersect more then once and less than an infinite number of times, it is easier to remember that if all you have are lines, there are only the 0, 1, or $\infty$ solution sets.

anonymous · Answer

Yep, thank-you very much.