My favorite method is elimination because its very easy and simple. Your not doing much but just finding the least common multiple and getting x or y by its self. Than you would distribute it into the numbers in the parenthesis and once you find your answer you would plug it in to find the next variable.
My least favorite method is graphing because it's hard trying to find the y-intercept. You have to solve the system of linear equations graphically we graph both equations in the same coordinates system. The solution to the system will be in the point where the two lines intersect. I think that's a lot of work