1) There's a lot of different methods for solving a system of equation. But here are my three favorite.
Graphing
Substitution (Which I preferred to use and I think it is easier).
Elimination
2) When solving a system of equations, you can get;
One solution
No solution
Infinite number of solution
3) The graphing method help solving a system of equation by knowing that the solution to a system of equations is the point of intersection of the two lines.
I hope this answer helps. As always, it is my pleasure helping student like you!