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The exercise provides two equations: one for demand and one for supply, and asks to determine the equilibrium price and quantity.

1. **Demand function**:  
   \[ Q_d = 100 - 6P \]
   
2. **Supply function**:  
   \[ Q_s = 30 + 4P \]

To find the **equilibrium**, we set the quantity demanded (\(Q_d\)) equal to the quantity supplied (\(Q_s\)):

\[
100 - 6P = 30 + 4P
\]

### Step-by-step solution:

1. **Move all terms involving \(P\) to one side**:
   \[
   100 - 30 = 4P + 6P
   \]
   \[
   70 = 10P
   \]

2. **Solve for \(P\)** (equilibrium price):
   \[
   P = \frac{70}{10} = 7
   \]

So, the equilibrium price is \(P = 7\).

3. **Substitute \(P = 7\) back into either the demand or supply function to find the equilibrium quantity**. Using the demand function:
   \[
   Q_d = 100 - 6(7) = 100 - 42 = 58
   \]

Thus, the equilibrium quantity is \(Q = 58\).

### Final Answer:
- Equilibrium price: \(P = 7\)
- Equilibrium quantity: \(Q = 58\)

Do you need more details or have any questions?

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Here are 5 related questions you could explore:
1. What happens to the equilibrium price if the supply function changes to \(Q_s = 40 + 5P\)?
2. How would a tax on the good affect the equilibrium price and quantity?
3. What is the impact of a price ceiling set below the equilibrium price?
4. How does an increase in demand (e.g., \(Q_d = 120 - 6P\)) affect the new equilibrium?
5. What is the price elasticity of demand at the equilibrium point?

**Tip**: Always set the demand equal to supply to find the equilibrium in a market problem.

La función de demanda para un bien es Qd = 100 - 6P y la función de oferta es Qs = 30 + 4P. Determina el precio y la cantidad de equilibrio.

Learn how to determine the equilibrium price and quantity for a good using the linear demand function Qd = 100 - 6P and supply function Qs = 30 + 4P. This step-by-step guide is suitable for high school or early college students studying economics or algebra.

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