Newbie question - Can Maxima be used to "manually" solve systems of equations

I was originally referred to Maxima for its plotting capabilities. That 
need has gone away, but I've started looking at solving systems of 
equations which is more its intended purpose.

*BUT*
In order to review algebra I haven't thought about in over 40 years, I 
wished to manually solve a _simplified idealized_ case first.

System is idealized GPS system where all satellite and ground receiver 
are perfectly stable and perfectly synchronized.

I then have a system of 3 quadratic equations in 3 unknowns.
I wish to solve it by a method whose name I can't recall.
[subtracting multiple of one equation from another such that matrix 
representation has only 0's below the diagonal]

I can do this with pencil and paper, but have poor handwriting and I 
would end up losing things. Maxima does clean presentation of algebra.

In a way I wish to use it as an intelligent algebraicly aware notepad.exe.

A related question - recommended introductory survey of uses of Maxima. 
What I have found so fare are either very detailed documentation or 
intros which the author wishes to take some one from a specific point to 
the author's intended destination.

TIA