Question

The sum of two integers is 2. The difference is 10. What are the two integers?

Answer 1

Let's denote the two integers as \( x \) and \( y \). According to the problem, we have the following two equations:

1. \( x + y = 2 \)
2. \( x - y = 10 \)

We can solve these equations step by step.

First, we can add the two equations together:

\[
(x + y) + (x - y) = 2 + 10
\]

This simplifies to:

\[
2x = 12
\]

Dividing both sides by 2 gives:

\[
x = 6
\]

Now, we can substitute \( x \) back into the first equation to find \( y \):

\[
6 + y = 2
\]

Subtracting 6 from both sides results in:

\[
y = 2 - 6 = -4
\]

Thus, the two integers are \( x = 6 \) and \( y = -4 \).

To summarize, the integers are \( \boxed{6} \) and \( \boxed{-4} \).