Solve :
`(3)/(x) + (2)/(y) = 10`
`(9)/(x) - (7)/(y) = 105`

Answer

To solve the simultaneous equations:

1. \( \frac{3}{x} + \frac{2}{y} = 10 \) (Equation 1)
2. \( \frac{9}{x} - \frac{7}{y} = 10.5 \) (Equation 2)

### Step 1: Rewrite the equations
Let's rewrite the equations for clarity:

- Equation 1: \( \frac{3}{x} + \frac{2}{y} = 10 \)
- Equation 2: \( \frac{9}{x} - \frac{7}{y} = 10.5 \)

### Step 2: Multiply Equation 1 by 3
To eliminate \( \frac{9}{x} \) in the second equation, we can multiply Equation 1 by 3:

\[ 3 \left( \frac{3}{x} + \frac{2}{y} \right) = 3 \cdot 10 \]

This gives us:

\[ \frac{9}{x} + \frac{6}{y} = 30 \quad \text{(Equation 3)} \]

### Step 3: Subtract Equation 2 from Equation 3
Now, we subtract Equation 2 from Equation 3:

\[ \left( \frac{9}{x} + \frac{6}{y} \right) - \left( \frac{9}{x} - \frac{7}{y} \right) = 30 - 10.5 \]

This simplifies to:

\[ \frac{6}{y} + \frac{7}{y} = 30 - 10.5 \]

Combining the fractions on the left side gives:

\[ \frac{13}{y} = 19.5 \]

### Step 4: Solve for \( y \)
Now, we can solve for \( y \):

\[ y = \frac{13}{19.5} \]

To simplify \( \frac{13}{19.5} \), we can multiply the numerator and the denominator by 10 to eliminate the decimal:

\[ y = \frac{130}{195} \]

Now, simplifying \( \frac{130}{195} \) gives:

\[ y = \frac{2}{3} \]

### Step 5: Substitute \( y \) back into Equation 1
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):

\[ \frac{3}{x} + \frac{2}{\frac{2}{3}} = 10 \]

This simplifies to:

\[ \frac{3}{x} + 3 = 10 \]

### Step 6: Solve for \( x \)
Now, isolate \( \frac{3}{x} \):

\[ \frac{3}{x} = 10 - 3 \]

This gives:

\[ \frac{3}{x} = 7 \]

Now, solving for \( x \):

\[ x = \frac{3}{7} \]

### Final Solution
Thus, the solution to the simultaneous equations is:

\[ x = \frac{3}{7}, \quad y = \frac{2}{3} \]