Consider the market for compact cars as an example, where 'P' stands for the price of a compact car in thousands of dollars. We can model the quantity demanded (Q_d) and quantity supplied (Q_s) with the following linear equations:

Quantity Demanded for Compact Cars: Q_d = 60−3P

Quantity Supplied for Compact Cars: Q_s = 20+2P

At market equilibrium, Q_d = Q_s.

By setting these two equations equal to each other, we can solve for 'P', the equilibrium price: 60−3P = 20+2P

Solving this equation gives us the equilibrium price, which is P=8 thousand dollars.

Substituting this price back into either the demand or supply equation yields the equilibrium quantity. For instance, the market will balance at 36 million compact cars. This represents the point at which the supply of compact cars perfectly meets consumer demand.

It's important to recognize that this simplified model assumes other factors remain constant. In the real world, supply and demand are influenced by many factors, such as economic conditions, consumer preferences, and technological innovations, which can alter the relationship between the market price and the quantity demanded or the quantity supplied. This would shift one or both of these curves and thus affect market equilibrium.