Eliminating time (t) between two equations

[ohms law]

I'm working through several example problems, and one thing that has come up a couple of times is where the person who solved these problems says "Eliminating t between equations (1)
and (2) yields", or something similar. He's deriving an equation based on two other equations obviously, but I don't understand how or why (well, I sort of understand why, but...)

So, in this instance, equation (1) is:
$x=V_{0x}t=(V_{0}Cos\Theta_{0})t$

Equation (2) is:
$y=y_{0}+V_{0y}t+{1/2}a_{y}t^{2}$

So, smashing them together (however you do that) and "eliminating t" (whatever that means, beyond the obvious), yields:
$y=y_{0}+(Tan\Theta_{0})x+({a_{y}/2v_{0}^{2}Cos^{2}\Theta_{0}})$
I mean... I basically have that memorized now, but... how?

 

[SHISHKABOB]

it looks like he solved for t in the first equation and then substituted that in for t in equation 2

 

[azizlwl]

Notes on parametric equations.
http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx

 

[ohms law]

ooooh, parametric equations... haven't started those yet (in my calc class).
Thanks azizlwl!

That's actually a good insight too, shishkabob.
So, thanks to both of you.

(actually, after skimming through that parametric equations tutorial, I think that we've started on this material... some of it, anyway. humm...)