Linear systems... algebra?

Question

When graphing linear systems... there's intersecting lines, coinciding lines, and parallel lines.

What do they mean when they say that one line has no unique solution?

Answer 1

It's been a while since I studied this in school, but I believe it means, that unlike a point, a line has a set of relevant solutions. For instance, a point (1,5,1) is the only possible (+ integral) solution to x + (1/5)y + z = 3. However, when solving for y=, you can still get a variety of answers, all of which would fall along the line.
In this case, y=5*(3-x-z) = 15 - 5x - 5z. With y=0, you have x=1 & z=2 or x=2 & z=1, etc.

So......confused yet? I am. I believe what I'm trying to say is that along the line, any particular point can satisfy the equation, meaning that it has no unique solution where any single point is the only answer. That only works if y is equal to a number, as are x & z.

Good luck. I hope this helps.