is it true or false if two lines with infinitely many solutions are parallel

Question

mertsj · Answer

Now just think for a minute.

mertsj · Answer

When you find the solution of two lines, what are you finding?

anonymous · Answer

if its true why?

mertsj · Answer

Could you answer my question?

anonymous · Answer

im finding the x and y intercept?

mertsj · Answer

Well, I don't think that is quite it.  Look at this drawing:

anonymous · Answer

yes

mertsj · Answer

|dw:1366337437731:dw|

anonymous · Answer

im looking for the point where the lines intersect?

mertsj · Answer

If I graph two lines, the solution of the system is the point where they cross.  In the drawing...point A.  Does this sound familiar?

anonymous · Answer

yes a little bit.

mertsj · Answer

So how many solutions are there in the picture I drew?

anonymous · Answer

Many solutions?

mertsj · Answer

So the two lines cross each other in lots of places?

anonymous · Answer

No nevermind its only one solution.

mertsj · Answer

Yes.  Now if the lines were parallel, how many times would they cross?

anonymous · Answer

None!

mertsj · Answer

So how many solutions would there be?

anonymous · Answer

no solutions

mertsj · Answer

So what is the answer to the question you posted?

anonymous · Answer

the answer is false because the lines dont cross

mertsj · Answer

Yes it is false.  Good job.

anonymous · Answer

thanks! What needs to be true of the two equations in order for the system to have no solution

mertsj · Answer

Well, as we discussed, if the lines are parallel, there is no solution.  What do you know about the slopes of parallel lines?

anonymous · Answer

the slopes are the same

mertsj · Answer

So you have just answered your own question...

anonymous · Answer

ohh hahaa