Solve for x and y:
x + 2y = 9
2x - y = 8

Answer

To solve the system of equations:

1. **Equations:**
\[ x + 2y = 9 \quad \text{(Equation 1)} \]
\[ 2x - y = 8 \quad \text{(Equation 2)} \]

2. **Step 1: Multiply Equation 1 by 2.**
\[ 2(x + 2y) = 2(9) \]
This gives us:
\[ 2x + 4y = 18 \quad \text{(Equation 3)} \]

3. **Step 2: Now we have two equations:**
\[ 2x + 4y = 18 \quad \text{(Equation 3)} \]
\[ 2x - y = 8 \quad \text{(Equation 2)} \]

4. **Step 3: Subtract Equation 2 from Equation 3.**
\[ (2x + 4y) - (2x - y) = 18 - 8 \]
Simplifying this gives:
\[ 2x + 4y - 2x + y = 10 \]
\[ 5y = 10 \]

5. **Step 4: Solve for \( y \).**
\[ y = \frac{10}{5} = 2 \]

6. **Step 5: Substitute \( y = 2 \) back into Equation 1 to find \( x \).**
\[ x + 2(2) = 9 \]
\[ x + 4 = 9 \]
\[ x = 9 - 4 = 5 \]

7. **Final Solution:**
\[ x = 5, \quad y = 2 \]