Solve :
`5x + (8)/(y) = 19`
`3x - (4)/(y) = 7`

Answer

To solve the simultaneous equations:

1. **Write down the equations:**
\[ 5x + \frac{8}{y} = 19 \quad \text{(Equation 1)} \]
\[ 3x - \frac{4}{y} = 7 \quad \text{(Equation 2)} \]

2. **Multiply Equation 2 by 2 to eliminate the fraction:**
\[ 2(3x - \frac{4}{y}) = 2(7) \]
This gives us:
\[ 6x - \frac{8}{y} = 14 \quad \text{(Equation 3)} \]

3. **Now, add Equation 1 and Equation 3:**
\[ (5x + \frac{8}{y}) + (6x - \frac{8}{y}) = 19 + 14 \]
Simplifying this, we have:
\[ 5x + 6x + \frac{8}{y} - \frac{8}{y} = 33 \]
Which simplifies to:
\[ 11x = 33 \]

4. **Solve for \(x\):**
\[ x = \frac{33}{11} = 3 \]

5. **Substitute \(x = 3\) back into Equation 1 to find \(y\):**
\[ 5(3) + \frac{8}{y} = 19 \]
This simplifies to:
\[ 15 + \frac{8}{y} = 19 \]

6. **Isolate \(\frac{8}{y}\):**
\[ \frac{8}{y} = 19 - 15 \]
\[ \frac{8}{y} = 4 \]

7. **Solve for \(y\):**
\[ y = \frac{8}{4} = 2 \]

8. **Final solution:**
\[ x = 3, \quad y = 2 \]