So, what the heck is something like
Well, when we have two variables, x and y, we have a line... and we graph them on a 2-dimensional plane. So, with three variables, x, yand z, we'll be in three dimensions... That's 3-D space!
|Pretend that the floor of the room you are in is our old x-y plane...|
|The third dimension will be the vertical line shooting up from the corner of the room.|
This is really all you need to worry about... unless you're going to take Calculus 3. (Which is a very cool class, by the way! Cough - geek!)
So, an equation like
is a plane that lives in 3-D space.
With a system of three equations and three unknowns, we've got three planes in 3-D space. Look in the corner of your room again... That little corner is THE one point where the two walls and the floor (or the ceiling -- depending on where you're looking) intersect.
|So, hopefully, we'll get a nice |
(x, y, z) point like (1, -2, 4)for an answer.
(Check out the "Freaky Things" lesson!)
This means that x = 1, y = -2, z = 4 will work in ALL three of the original equations you started with.