To find the general equilibrium prices (and quantities) in practice, we must simultaneously find two prices that equate quantity demanded and quantity supplied in all related markets.
For our two markets, we need to find the solution to four equations (supply of movie tickets, demand for movie tickets, supply of DVDs, and demand for DVDs).
Movies and DVDs are substitute goods. If the goods in question are complements, a partial equilibrium analysis will overstate the impact of a tax.