Write a pair of integers whose sum is zero (0) but difference is 10.

Answer

To find a pair of integers whose sum is 0 and difference is 10, we can follow these steps:

### Step 1: Understand the requirements
We need to find two integers, let's call them \( x \) and \( y \), such that:
1. Their sum \( x + y = 0 \)
2. Their difference \( x - y = 10 \)

### Step 2: Express one integer in terms of the other
From the first equation \( x + y = 0 \), we can express \( y \) in terms of \( x \):
\[ y = -x \]

### Step 3: Substitute \( y \) in the difference equation
Now, substitute \( y \) in the second equation \( x - y = 10 \):
\[ x - (-x) = 10 \]
This simplifies to:
\[ x + x = 10 \]
\[ 2x = 10 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{10}{2} = 5 \]

### Step 5: Find \( y \)
Now that we have \( x \), we can find \( y \) using the expression we derived:
\[ y = -x = -5 \]

### Step 6: State the pair of integers
Thus, the pair of integers we are looking for is \( (5, -5) \).

### Verification
1. **Sum**: \( 5 + (-5) = 0 \) (which satisfies the first condition)
2. **Difference**: \( 5 - (-5) = 5 + 5 = 10 \) (which satisfies the second condition)

### Final Answer
The required pair of integers is \( (5, -5) \).

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