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The method is the same.
The correct spelling is "algorithm" (a method of expressing and solving equations).
The solution is the coordinates of the point where the graphs of the equations intersect.
Substitution is a way to solve without graphing, and sometimes there are equations that are impossible or very difficult to graph that are easier to just substitute. Mostly though, it is a way to solve if you have no calculator or cannot use one (for a test or worksheet).
The graphical method is a method used to solve algebraical problems by using graphs.