Equilibrium price and quantity from two lines

Statement

In a market the demand price is $P_d=25-Q$ and the supply price is $P_s=2Q+1$ (in €). Find the equilibrium quantity and price.

Solution

At equilibrium $P_d=P_s$: $25-Q=2Q+1\iff 24=3Q\iff Q^{*}=8.$ Price: $P^{*}=25-8=17\ \text{€}$. $\boxed{(Q^{*};\,P^{*})=(8;\,17\ \text{€})}$