It seems like you have two equations, likely representing demand and supply in a market. Let's label them properly:

1. **Demand equation**: \( Q_d = 50 - 2p \)
2. **Supply equation**: \( Q_o = 10 + 3p \)

Here:

- \( Q_d \) represents the quantity demanded.
- \( Q_o \) represents the quantity supplied.
- \( p \) represents the price.

### To find the equilibrium price and quantity:

The equilibrium occurs where quantity demanded equals quantity supplied, i.e., \( Q_d = Q_o \).

So, set the equations equal to each other:

\[
50 - 2p = 10 + 3p
\]

### Solving for \( p \):

1. Add \( 2p \) to both sides:
   \[
   50 = 10 + 5p
   \]

2. Subtract 10 from both sides:
   \[
   40 = 5p
   \]

3. Divide by 5:
   \[
   p = 8
   \]

### Find the equilibrium quantity:

Substitute \( p = 8 \) back into either equation (let's use the demand equation):

\[
Q_d = 50 - 2(8) = 50 - 16 = 34
\]

So, the equilibrium price \( p \) is 8, and the equilibrium quantity \( Q \) is 34.

### Summary:
- **Equilibrium Price (\( p \))**: 8
- **Equilibrium Quantity (\( Q \))**: 34

Would you like more details or have any other questions?

### Related Questions:
1. How would the equilibrium change if the demand equation changes to \( Q_d = 60 - 2p \)?
2. What happens to the equilibrium price and quantity if the supply equation changes to \( Q_o = 5 + 3p \)?
3. How would a price ceiling below the equilibrium price affect the market?
4. Can you find the consumer surplus at the equilibrium price?
5. How does the elasticity of demand affect the equilibrium price?

**Tip:** In economics, when solving for equilibrium, always set the demand equal to the supply to find the price and quantity where the market clears.

Learn how to find the equilibrium price and quantity in supply and demand analysis using mathematical equations. Explore detailed step-by-step solutions to balance quantity demanded and supplied equations. Suitable for advanced high school students studying economics and mathematics.

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