Example 1

The demand function of a good is given by $q_d(p)=10-p$, $(p\geq 0)$ and the supply function by $q_s(p)=2p+1$, $(p\geq 0)$. We determine the market equilibrium.

This implies the following:
$$\begin{align} q_d(p)=q_s(p)& \Leftrightarrow 10-p=2p+1\\ & \Leftrightarrow 9=3p\\ & \Leftrightarrow p=3. \end{align}$$

Since $q_d(3)=q_s(3)=7$ the market equilibrium is $(q,p)=(7,3)$.