Yes and no. It's more a matter of precision than substantially different answers.
If you solve graphically, then you can estimate solutions by simply reading the graph. However, the solutions precision is limited by the size of the graph, how good your eyes are, the width of your pencil lines, etc.
An algebraic solution yields exact answers.
For example, if a solution was , then that's what the algebraic method would give you, but graphically, you would get 1.4142136...
woot! it's been years since I used LaTeX, and I formatted the sqrt(2) above right on the first try!