Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best?

Since I suspect this is a homework question, I'm not going to outright answer it. You should think about it and see what you come up with. Plus it apparently wants your opinion, not someone else's.

However, I will say that I'll probably disagree with whatever some book claims is the "best" method, simply because I think it always depends partially on the person doing it. Sometimes something is just easier for some particular person than something else, and unless there's a good reason not to, the easier way for them is then the "best" way. The easiest way for me to do something is the way I find and finish first. ;)

I do prefer elimination and find that most students I work with prefer it too -- they seem to dislike substitution.

For me, I preferred substitution when I learned about simultaneous equations. That was because I didn't understand elimination as it should be. Later, I gradually learned how to use it well and I now find it quite handy at times, for fast solving equations. Depending on the way the problem was put, I use one method or the other, no particular preference for me. :)

The graphing method is the most reliable one for me, since you see exactly the possible solutions, provided your sketch is quite appropriate, but it has got it's limitations for precise answers.