Here are a few points on supply-demand graphs; it is not always obvious why they are favoured over algebraic solutions, so the points may help clarify.
1. Simultaneous equations expressing market supply-demand behaviour are often not solved explicitly, but by plotting in graphs (so showing how a market mechanism would adjust to obtain the equilibrium)
2. The effect of parameter variation is shown by shifts in graphs and then stated verbally
3. The effect of assumption variation is shown by shifts in graphs and then stated verbally
4. The verbal descriptions of effects on graphs are explicit (“rotates curves”, “shifts curves out”). The curves and the quantities and behaviour they describe are treated as synonymous (“the money supply grows shifting the demand curve to the right, which in turn increases profits”)