If `x - y = 2` and `(2)/(x + y) = (1)/(5)` then x = ……..

Answer

To solve the equations \( x - y = 2 \) and \( \frac{2}{x + y} = \frac{1}{5} \) for the value of \( x \), follow these steps:

### Step 1: Rewrite the second equation
We start with the equation:
\[ \frac{2}{x + y} = \frac{1}{5} \]
To eliminate the fraction, we can cross-multiply:
\[ 2 \cdot 5 = 1 \cdot (x + y) \]
This simplifies to:
\[ 10 = x + y \]

### Step 2: Write down the system of equations
Now we have a system of two equations:
1. \( x - y = 2 \) (Equation 1)
2. \( x + y = 10 \) (Equation 2)

### Step 3: Add the two equations
Next, we can add Equation 1 and Equation 2:
\[ (x - y) + (x + y) = 2 + 10 \]
This simplifies to:
\[ 2x = 12 \]

### Step 4: Solve for \( x \)
Now, we can solve for \( x \) by dividing both sides by 2:
\[ x = \frac{12}{2} = 6 \]

### Step 5: Conclusion
Thus, the value of \( x \) is:
\[ \boxed{6} \]

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