Question 152479
Graphing gives you a good idea of where the solution but it's not exact. 
Elmination and substitution give you the exact answer but it can become tedious and cumbersome. 
An example, if the solution is x=3/7 and y=5/7, you'd get close with graphing 

(x=0.4, y=0.7 or x=0.43,y=0.71, depending on the fineness of your graphing paper) 
but you'd never get the exact answer.