The algebraic method is more useful when working with numbers and trying to solve for different things. These things could be x and y intercepts or points of intersection with other lines. Yet it doesn't offer the visual aid of graphs. The graphing method is useful because you can see where things intercept. It can check the answer of the algebraic function by easily looking at the graph and seeing if the answer makes sense. Of course the graphing method may not be as easy to see exact, small numbers as compared with the algebraic method.