Solve the following pair of equations:
`(x)/(3) + (y)/(4)= 4, (5x)/(6)-(y)/(8)=4`

Answer

To solve the given pair of equations:

1. **Equations**:
\[ \frac{x}{3} + \frac{y}{4} = 4 \quad \text{(Equation 1)} \]
\[ \frac{5x}{6} - \frac{y}{8} = 4 \quad \text{(Equation 2)} \]

2. **Clear the fractions**:
- For Equation 1, multiply through by 12 (the least common multiple of 3 and 4):
\[ 12 \left(\frac{x}{3}\right) + 12 \left(\frac{y}{4}\right) = 12 \cdot 4 \]
This simplifies to:
\[ 4x + 3y = 48 \quad \text{(Equation 3)} \]

- For Equation 2, multiply through by 24 (the least common multiple of 6 and 8):
\[ 24 \left(\frac{5x}{6}\right) - 24 \left(\frac{y}{8}\right) = 24 \cdot 4 \]
This simplifies to:
\[ 20x - 3y = 96 \quad \text{(Equation 4)} \]

3. **Now we have a new system of equations**:
\[ 4x + 3y = 48 \quad \text{(Equation 3)} \]
\[ 20x - 3y = 96 \quad \text{(Equation 4)} \]

4. **Add Equation 3 and Equation 4**:
\[ (4x + 3y) + (20x - 3y) = 48 + 96 \]
This simplifies to:
\[ 24x = 144 \]
Dividing both sides by 24 gives:
\[ x = 6 \]

5. **Substitute \(x = 6\) back into Equation 3 to find \(y\)**:
\[ 4(6) + 3y = 48 \]
This simplifies to:
\[ 24 + 3y = 48 \]
Subtracting 24 from both sides gives:
\[ 3y = 24 \]
Dividing both sides by 3 gives:
\[ y = 8 \]

6. **Final Solution**:
The solution to the system of equations is:
\[ x = 6, \quad y = 8 \]