Suppose, we have the following demand and supply relationships:
        Demand: Q_D = 120 - 2P
        Supply: Q_S = -30 + P

We found before that, for this market, equilibrium price and quantity are:
        P = 50 and
        Q = 20

Now, suppose demand shifts back so that the new demand relationship is:
        Q_D2 = 90 - 2P

We can solve for the new equilibrium:
        90 - 2P = -30 + P
        120 = 3P
        P = 40
        Q = 10

Our simple demand and supply system confirms the result of our graphical analysis: When demand decreases (shifts back), equilibrium price and quantity both fall.