Solve :
` 3x+ 2y = 14`
` - x+ 4y = 7 `

Answer

To solve the system of equations:

1. **Equations Given**:
\[ 3x + 2y = 14 \quad \text{(1)} \]
\[ -x + 4y = 7 \quad \text{(2)} \]

2. **Multiply Equation (1)** by 2 to align the coefficients of \(y\):
\[ 2(3x + 2y) = 2(14) \]
This results in:
\[ 6x + 4y = 28 \quad \text{(3)} \]

3. **Now we have the modified equations**:
\[ 6x + 4y = 28 \quad \text{(3)} \]
\[ -x + 4y = 7 \quad \text{(2)} \]

4. **Subtract Equation (2) from Equation (3)**:
\[ (6x + 4y) - (-x + 4y) = 28 - 7 \]
This simplifies to:
\[ 6x + 4y + x - 4y = 21 \]
Which further simplifies to:
\[ 7x = 21 \]

5. **Solve for \(x\)**:
\[ x = \frac{21}{7} = 3 \]

6. **Substitute \(x = 3\) back into Equation (2)** to find \(y\):
\[ -3 + 4y = 7 \]
Adding 3 to both sides gives:
\[ 4y = 10 \]

7. **Solve for \(y\)**:
\[ y = \frac{10}{4} = 2.5 \]

8. **Final Solution**:
\[ x = 3, \quad y = 2.5 \]