The problem asks us to find the market equilibrium point $(q, p)$ given the demand and supply functions: Demand: $2p = -q + 81$ Supply: $3p - q = 69$

1. Problem Description

The problem asks us to find the market equilibrium point $(q, p)$ given the demand and supply functions:

Demand: $2p = -q + 81$

Supply: $3p - q = 69$

2. Solution Steps

We have a system of two equations with two variables $p$ and $q$.

$2p = -q + 81$

$3p - q = 69$

From the first equation, we can express $q$ in terms of $p$:

$q = 81 - 2p$

Now we substitute this expression for $q$ into the second equation:

$3p - (81 - 2p) = 69$

$3p - 81 + 2p = 69$

$5p = 69 + 81$

$5p = 150$

$p = \frac{150}{5}$

$p = 30$

Now that we have the value of $p$, we can substitute it back into the equation $q = 81 - 2p$ to find $q$:

$q = 81 - 2(30)$

$q = 81 - 60$

$q = 21$

Therefore, the equilibrium point is $(q, p) = (21, 30)$.

3. Final Answer

(21, 30)