Let's consider the problem at hand with the given set of values:
[tex]\[
\begin{array}{llllll}3 & 28 & 8 & 17 & 4 & 101\end{array}
\][/tex]
We want to find two numbers from this set such that their sum equals a particular target value, which we will denote as [tex]\(y\)[/tex]. The condition given is [tex]\(y \neq 0\)[/tex].
Step-by-Step Solution:
1. First, we list the pairs and their sums:
- [tex]\(3 + 28 = 31\)[/tex]
- [tex]\(3 + 8 = 11\)[/tex]
- [tex]\(3 + 17 = 20\)[/tex]
- [tex]\(3 + 4 = 7\)[/tex]
- [tex]\(3 + 101 = 104\)[/tex]
- [tex]\(28 + 8 = 36\)[/tex]
- [tex]\(28 + 17 = 45\)[/tex]
- [tex]\(28 + 4 = 32\)[/tex]
- [tex]\(28 + 101 = 129\)[/tex]
- [tex]\(8 + 17 = 25\)[/tex]
- [tex]\(8 + 4 = 12\)[/tex]
- [tex]\(8 + 101 = 109\)[/tex]
- [tex]\(17 + 4 = 21\)[/tex]
- [tex]\(17 + 101 = 118\)[/tex]
- [tex]\(4 + 101 = 105\)[/tex]
2. Having computed all these sums, we can check if there exists any pair that results in a target sum equal to a certain value [tex]\(y\)[/tex] that isn't zero.
3. By reviewing the possible sums:
- 7, 11, 12, 20, 21, 25, 31, 32, 36, 45, 104, 105, 109, 118, 129
4. However, we see that none of these sums match our goal if our target sum was, for example, 30 (which would imply [tex]\(x + y = 30\)[/tex]). This means no pair of these values can satisfy such an equation with the target sum [tex]\(y\)[/tex].
Therefore, after considering all these sums and pairs given the set of values and aiming for a specific target sum, we can conclude:
[tex]\[
\text{No pair found that fits the target sum with the given condition}
\][/tex]
Thus, there are no two numbers in this set that will satisfy any equation of the form [tex]\( x + y = 30 \)[/tex].
