the 3 methods used in solving a system of equations is : substitution, elimination, and matrices.  which method do I prefer.....depends on the equations.  if they are : x + y = 2....and x - y = 4....then I prefer elimination... because u can just add them eliminating the y. but if it is like : y = 2x and x + y = 4....then I prefer substitution. I am not good at matrices...so I dont usually use them....but I believe they are pretty similar to elimination...and shorter. Elimination takes many steps and if u mess up on a beginning step, it carries through to the end.