Solve for x and y:

7x - 4y = 49
5x - y = 22

Answer

To solve the system of equations:

1. **Equations:**
\[ 7x - 4y = 49 \quad \text{(Equation 1)} \]
\[ 5x - y = 22 \quad \text{(Equation 2)} \]

2. **Rearranging the equations:**
We can keep them as they are for solving, but let's label them for clarity:
- Equation 1: \( 7x - 4y = 49 \)
- Equation 2: \( 5x - y = 22 \)

3. **Using the elimination method:**
We will eliminate \( y \) by making the coefficients of \( y \) in both equations equal. To do this, we can multiply Equation 2 by 4:
\[ 4(5x - y) = 4(22) \]
This gives us:
\[ 20x - 4y = 88 \quad \text{(Equation 3)} \]

4. **Now we have:**
- Equation 1: \( 7x - 4y = 49 \)
- Equation 3: \( 20x - 4y = 88 \)

5. **Subtract Equation 1 from Equation 3:**
\[ (20x - 4y) - (7x - 4y) = 88 - 49 \]
This simplifies to:
\[ 20x - 7x = 88 - 49 \]
\[ 13x = 39 \]

6. **Solving for \( x \):**
\[ x = \frac{39}{13} = 3 \]

7. **Substituting \( x \) back into Equation 2 to find \( y \):**
\[ 5x - y = 22 \]
Substitute \( x = 3 \):
\[ 5(3) - y = 22 \]
\[ 15 - y = 22 \]
\[ -y = 22 - 15 \]
\[ -y = 7 \]
\[ y = -7 \]

8. **Final solution:**
\[ x = 3, \quad y = -7 \]

### Summary:
The solution to the equations is:
\[ x = 3, \quad y = -7 \]