To find the possible values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] such that [tex]\( x + y = 3 \)[/tex], we need to find pairs of whole numbers that add up to 3. Let's go through the process step-by-step:
1. Identify the equation: We have the equation [tex]\( x + y = 3 \)[/tex].
2. List out all whole numbers from 0 to 3 (inclusive) for [tex]\( x \)[/tex], since [tex]\( x \)[/tex] and [tex]\( y \)[/tex] must be whole numbers:
[tex]\[
x \in \{0, 1, 2, 3\}
\][/tex]
3. Calculate corresponding [tex]\( y \)[/tex] values:
For each [tex]\( x \)[/tex] value, solve for [tex]\( y \)[/tex] by rearranging the equation [tex]\( y = 3 - x \)[/tex].
- When [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 3 - 0 = 3
\][/tex]
Thus, one pair is [tex]\((0, 3)\)[/tex].
- When [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 3 - 1 = 2
\][/tex]
Thus, another pair is [tex]\((1, 2)\)[/tex].
- When [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 3 - 2 = 1
\][/tex]
Thus, another pair is [tex]\((2, 1)\)[/tex].
- When [tex]\( x = 3 \)[/tex]:
[tex]\[
y = 3 - 3 = 0
\][/tex]
Thus, the final pair is [tex]\((3, 0)\)[/tex].
4. List the possible pairs:
- [tex]\((0, 3)\)[/tex]
- [tex]\((1, 2)\)[/tex]
- [tex]\((2, 1)\)[/tex]
- [tex]\((3, 0)\)[/tex]
Therefore, three possible values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy [tex]\( x + y = 3 \)[/tex] are [tex]\( (0, 3) \)[/tex], [tex]\( (1, 2) \)[/tex], and [tex]\( (2, 1) \)[/tex]. In fact, these are all the possible pairs given our constraints.
