You are confusing two things.
A) You can do the N-R method by hand, or with simple calculator. You can use
Excel do all this step by step just as if you were doing it by hand
B) You can set up a model and have Solver find the answer. Solver does all
the hard work including the matrix stuff.
If your chem prof (I was one myself until 3 months ago) is asking you do
solve thermodynamics by A, he/she is a dodo. Does he ask you to use the N-R
method to find square roots?
If she/he is a math prof then you should learn the step by step method. See
Help fro MDERTM, MINVERSE, MMULT
(Then use Solver to check your math!)
Send me private email and I will send you a PDF file on using the matrix
functions to solve systems of equations (aka simultaneous equations)