If `x -y =- 7 and x + y = 13,` then `x ^(2) - y ^(2)` is

Options

A. 91
B. 30
C. `-30 `
D. `-91`

Answer

To solve the problem, we need to find the value of \( x^2 - y^2 \) given the equations \( x - y = -7 \) and \( x + y = 13 \).

### Step-by-Step Solution:

1. **Identify the equations**:
We have two equations:
\[ x - y = -7 \quad \text{(1)} \]
\[ x + y = 13 \quad \text{(2)} \]

2. **Use the difference of squares formula**:
We know that:
\[ x^2 - y^2 = (x - y)(x + y) \]
We can substitute the values from equations (1) and (2) into this formula.

3. **Substitute the values**:
From equation (1), \( x - y = -7 \) and from equation (2), \( x + y = 13 \). Therefore,
\[ x^2 - y^2 = (x - y)(x + y) = (-7)(13) \]

4. **Calculate the product**:
Now we calculate:
\[ -7 \times 13 = -91 \]

5. **Final result**:
Therefore, we have:
\[ x^2 - y^2 = -91 \]

### Conclusion:
The value of \( x^2 - y^2 \) is \( -91 \).