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We are given two equations:
1. \( x^2 - y^2 = 2 \)
2. \( x - y = 1 \)

We need to find \( x + y \).

### Step-by-Step Solution:
1. **Factor the first equation**:
   \[
   x^2 - y^2 = (x - y)(x + y)
   \]
   So the first equation becomes:
   \[
   (x - y)(x + y) = 2
   \]

2. **Substitute the value of \( x - y \) from the second equation**:
   From equation 2, \( x - y = 1 \). Substitute this into the factored equation:
   \[
   (1)(x + y) = 2
   \]
   So:
   \[
   x + y = 2
   \]

Thus, the value of \( x + y \) is 2.

### Answer:
The correct answer is **(b) 2**.

Let me know if you'd like further details or have any questions! Here are five related questions for practice:

1. If \( x^2 - y^2 = 9 \) and \( x - y = 3 \), what is \( x + y \)?
2. Solve for \( x \) and \( y \) if \( x - y = 2 \) and \( x^2 - y^2 = 8 \).
3. Given \( x + y = 4 \) and \( x - y = 2 \), solve for \( x \) and \( y \).
4. If \( x - y = 1 \) and \( x + y = 5 \), find \( x^2 - y^2 \).
5. Solve \( x^2 - y^2 = 16 \) and \( x - y = 4 \) for \( x + y \).

### Tip:
When you see expressions like \( x^2 - y^2 \), always try factoring them into \( (x - y)(x + y) \), which simplifies the problem.

If x^2 - y^2 = 2 and x - y = 1, then what is x + y?

Learn how to solve for x + y given the equation x^2 - y^2 = 2 and x - y = 1. This problem uses algebraic techniques like factoring and the difference of squares theorem. Suitable for students in Grades 8-10.

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