Find the market equilibrium point for the following demand and supply functions. Demand: \( \quad 2 p=-q+45 \) Supply: \( \quad 3 p-q=20 \) \( (q, p)=(\square \)

To find the market equilibrium point, we need to set the demand function equal to the supply function and solve for the values of \( q \) and \( p \). Given: Demand function: \( 2p = -q + 45 \) Supply function: \( 3p - q = 20 \) Setting the demand function equal to the supply function: \[ 2p = -q + 45 \] \[ 3p - q = 20 \] Now, we can solve this system of equations to find the values of \( q \) and \( p \) at the market equilibrium point. Let's solve the system of equations. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2p=-q+45\\3p-q=20\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}2p=-q+45\\q=-20+3p\end{array}\right.\) - step2: Substitute the value of \(q:\) \(2p=-\left(-20+3p\right)+45\) - step3: Simplify: \(2p=65-3p\) - step4: Move the variable to the left side: \(2p+3p=65\) - step5: Add the terms: \(5p=65\) - step6: Divide both sides: \(\frac{5p}{5}=\frac{65}{5}\) - step7: Divide the numbers: \(p=13\) - step8: Substitute the value of \(p:\) \(q=-20+3\times 13\) - step9: Simplify: \(q=19\) - step10: Calculate: \(\left\{ \begin{array}{l}p=13\\q=19\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}p=13\\q=19\end{array}\right.\) - step12: Rewrite: \(\left(p,q\right) = \left(13,19\right)\) The market equilibrium point is at \( (p, q) = (13, 19) \).