Question

Whats the best way to solve a 3 var. linear equation (requiring the least effort)

Answer 1

TI-84 RREF matrix function.

Answer 2

I assume you mean a three-equation, three-variable system, right?

Answer 3

i mean without the use of a calc

Answer 4

yups

Answer 5

It depends on the system..
Some have a variable that eliminates easily, others will fall apart nicely after enough substitution.
Matrix methods work fine and are low-effort if you have practice with them and can handle a lot of arithmetic steps quickly.