Using substitution method, If ` x - y = 2` and `(2)/(x + y ) = (1)/(5)` then

Options

A. ` x = 4, y = 2 `
B. `x = 5, y = 3 `
C. ` x = 6, y = 4`
D. ` x = 7, y = 5 `

Answer

To solve the given equations using the substitution method, we will follow these steps:

### Step 1: Write down the equations
We have two equations:
1. \( x - y = 2 \) (Equation 1)
2. \( \frac{2}{x + y} = \frac{1}{5} \) (Equation 2)

### Step 2: Simplify Equation 2
To simplify Equation 2, we will cross-multiply:
\[ 2 \cdot 5 = 1 \cdot (x + y) \]
This gives us:
\[ 10 = x + y \quad \text{(Equation 3)} \]

### Step 3: Express one variable in terms of the other
From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = y + 2 \quad \text{(Equation 4)} \]

### Step 4: Substitute Equation 4 into Equation 3
Now we will substitute \( x \) from Equation 4 into Equation 3:
\[ 10 = (y + 2) + y \]
This simplifies to:
\[ 10 = 2y + 2 \]

### Step 5: Solve for \( y \)
Now, we will isolate \( y \):
\[ 10 - 2 = 2y \]
\[ 8 = 2y \]
\[ y = \frac{8}{2} = 4 \]

### Step 6: Substitute \( y \) back to find \( x \)
Now that we have \( y \), we can find \( x \) using Equation 4:
\[ x = y + 2 = 4 + 2 = 6 \]

### Final Answer
Thus, the values of \( x \) and \( y \) are:
\[ x = 6, \quad y = 4 \]