Question

How do you know a system is on the same line or a parallel line if it has infinite or no solutions?

Answer 1

Do you mean a system of two equations?

Answer 2

Yes. Should I write down the problem?

Answer 3

Maybe it would help to make sure you understand what `solutions` means.
Solutions really means `points of intersection`.

Answer 4

Oh it seems you probably get that, you wrote the part about parallel lines. :p

Answer 5

sec, ill let larry get this one :p

Answer 6

Oh he vanished +_+

Answer 7

When you solve the system,

You'll have infinite solutions when you end with something like 0=0
or 1=1 or whatever.

See how everything cancelled out?
It means you can plug any value in for x and y and system will still hold true.
Infinite number of solutions.

If you instead end with something like 1=0
then your system is untrue for all values of x and y ( or whatever variables you're using ).
No solution to the system.

Answer 8

Or you can go the more traditional route, write the lines in slope-intercept form.
If they have the `same slope`, then they're parallel, no solutions (unless they have the same slope AND same y-intercept, then infinite solutions since they're the same line ).

Answer 9

Okay thanks so much!

Answer 10

no probs, sheesh that's quite the stache +_+