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To find the equilibrium price and quantity for products 1 and 2, we need to set the demand equations equal to the supply equations for each product. This will allow us to solve for the quantities \( q_1 \) and \( q_2 \), and then we can substitute these values back into the price equations.

### Given Equations

**For Product 1:**
1. Demand: \( P_1 = 2000 - 3q_1 - 2q_2 \)
2. Supply: \( P_1 = 100 + 2q_1 + q_2 \)

**For Product 2:**
3. Demand: \( P_2 = 2800 - q_1 - 4q_2 \)
4. Supply: \( P_2 = 200 + 3q_1 + 2q_2 \)

### Steps to Solve

1. **Set Demand equal to Supply for each product.**

   - For Product 1:
     \[
     2000 - 3q_1 - 2q_2 = 100 + 2q_1 + q_2
     \]
   - For Product 2:
     \[
     2800 - q_1 - 4q_2 = 200 + 3q_1 + 2q_2
     \]

2. **Simplify the equations.**

   - For Product 1:
     \[
     2000 - 100 = 2q_1 + 3q_1 + q_2 + 2q_2
     \]
     simplifies to

Find the equilibrium price and quantity for product 1 & 2.

Learn how to find the equilibrium price and quantity for two products by solving a system of linear equations. This problem involves setting demand equal to supply for each product and solving for the equilibrium quantities. Key algebraic concepts and equilibrium analysis methods are used.

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