Why is graphing not always the best option for solving systems?

1, Might not be precise 
2, Can be hard to plot the graphs
3, If there are many solutions that will be really hard to plot sometimes. 

This is just from the top of my head. 

Best   When graphing and locating the point of intersection & hence the solution, you might find that this point does not have integer co ordinates. You would have to estimate the approximate coordinates. Hence, the algebraic methods are preferred, as you could then state the exact co ordinates like (5/3, 4/9).