Tips on how can I make a program that would give me the 6 unknowns of 6 equations using the C++ language.?

Answer 1

My very best tip would be..... Don't.
Don't waste your time 're-inventing' somethig that has a thousand off-the-shelf, 'canned' solutions. The only time it makes sense to write a matrix reduction package is when it's been given to you as a class assignment. (Or if you're being paid an obscene amount of money ☺)
If that's the case, I'd suggest that you stick to a 'plain vanilla' matrix inversion routine (don't get fancy and start playing with variable pivot elements or succesive over-relaxation techniques. They work, but they're tricky ☺)

Doug