Question

Which pairs(s) of negative integers, x and y, make the statement x-y= -1 true?

Answer 1

To make the equation \( x - y = -1 \) true, we can rearrange the equation to find a relationship between \( x \) and \( y \):

\[
x - y = -1 \implies x = y - 1
\]

Since we are looking for pairs of negative integers \((x, y)\), we can choose a negative integer for \( y\) and calculate \( x\) accordingly.

Let's test some negative integers for \( y\):

1. If \( y = -1 \):
\[
x = -1 - 1 = -2 \quad \Rightarrow \quad (x, y) = (-2, -1)
\]

2. If \( y = -2 \):
\[
x = -2 - 1 = -3 \quad \Rightarrow \quad (x, y) = (-3, -2)
\]

3. If \( y = -3 \):
\[
x = -3 - 1 = -4 \quad \Rightarrow \quad (x, y) = (-4, -3)
\]

4. If \( y = -4 \):
\[
x = -4 - 1 = -5 \quad \Rightarrow \quad (x, y) = (-5, -4)
\]

Continuing this process, we can see a pattern. For any negative integer \( y\), we can always find a corresponding \( x\) by the formula \( x = y - 1 \).

So, valid pairs of negative integers \((x, y)\) that satisfy the equation \( x - y = -1 \) can be listed as follows:

- \((-2, -1)\)
- \((-3, -2)\)
- \((-4, -3)\)
- \((-5, -4)\)

In general:

The pairs of negative integers \( (x, y) \) satisfying \( x - y = -1 \) can be expressed as \((y - 1, y)\) for any negative integer \( y \).