# System of equations with multiple intersection points

• May 3rd 2009, 12:39 PM
Phire
System of equations with multiple intersection points
Hi, I was just wondering what happens when you've got a system of equations and multiple intersection points happen from those lines? For example:

http://i39.tinypic.com/eqts2q.gif

There seems to be more than 1 point between the two lines that intersect with each other. I am guessing that the system will solve into something that has a sort of equation for the Y variable? Such as: (x, 2x+1) ? And if I'm correct with that assumption, is there a way to find an interval for the range of valid x values?
• May 3rd 2009, 03:34 PM
Phire
Woops, the graph didn't show before. It should show up now.
• May 3rd 2009, 03:53 PM
VonNemo19
It seems that the graph of the two lines that you have given only intersects in one place. Do you have a graph to depict what you are trying to say? I'll gladly help if you do.
• May 3rd 2009, 04:17 PM
Phire
I thought that it might intersect at one more than one point, but I wasn't certain. Graphing this:

y = 3x+4 and y = 3.2x+4 looks like it may intersect at more than one point.

Is it even possible for two lines to intersect at more than one point if their slopes are not equal?
• May 3rd 2009, 04:25 PM
e^(i*pi)
Quote:

Originally Posted by Phire
I thought that it might intersect at one more than one point, but I wasn't certain. Graphing this:

y = 3x+4 and y = 3.2x+4 looks like it may intersect at more than one point.

Is it even possible for two lines to intersect at more than one point if their slopes are not equal?

I think it is because the graphs are too close for the graph to show. I'm pretty sure lines only intersect once if their gradients are different. In this case it would be (0,4)
• May 3rd 2009, 04:58 PM
VonNemo19
Two lines will intersect if they're slopes are not equal. There are NO exeptions to this rule, granted that the lines lie in the same plane.

If the slopes of two lines are equal and they lie in the same plane, they are either

a) parallel

b)overlapping

Does that help?
• May 4th 2009, 04:36 AM
stapel
Quote:

Originally Posted by Phire
Hi, I was just wondering what happens when you've got a system of equations and multiple intersection points happen from those lines? For example:

http://i39.tinypic.com/eqts2q.gif

There seems to be more than 1 point between the two lines that intersect with each other.

In the scraped image of a linear (that is, of a straight-line) system, where are you seeing one or another of the lines curving back to re-cross? (Wondering)
• May 4th 2009, 10:43 AM
Phire
I just made an incorrect assumption that linear equations could somehow touch in more than 1 place, but I know now that isn't possible.
• May 4th 2009, 10:45 AM
Phire
Quote:

Originally Posted by stapel
In the scraped image of a linear (that is, of a straight-line) system, where are you seeing one or another of the lines curving back to re-cross? (Wondering)

By the way, are you Elizabeth Stapel? (Hi)