Answer :
To determine if each ordered pair [tex]\((x, y)\)[/tex] is a solution to the equation [tex]\(y = 7\)[/tex], we need to check if the [tex]\(y\)[/tex]-coordinate of each pair equals 7. Let's go through each pair one by one:
1. Pair: [tex]\((6, 2)\)[/tex]
- Here, [tex]\(x = 6\)[/tex] and [tex]\(y = 2\)[/tex].
- Check if [tex]\(y = 7\)[/tex]: 2 is not equal to 7.
- Conclusion: [tex]\((6, 2)\)[/tex] is not a solution to [tex]\(y = 7\)[/tex].
2. Pair: [tex]\((7, -3)\)[/tex]
- Here, [tex]\(x = 7\)[/tex] and [tex]\(y = -3\)[/tex].
- Check if [tex]\(y = 7\)[/tex]: -3 is not equal to 7.
- Conclusion: [tex]\((7, -3)\)[/tex] is not a solution to [tex]\(y = 7\)[/tex].
3. Pair: [tex]\((-9, 7)\)[/tex]
- Here, [tex]\(x = -9\)[/tex] and [tex]\(y = 7\)[/tex].
- Check if [tex]\(y = 7\)[/tex]: 7 is equal to 7.
- Conclusion: [tex]\((-9, 7)\)[/tex] is a solution to [tex]\(y = 7\)[/tex].
4. Pair: [tex]\((-8, 0)\)[/tex]
- Here, [tex]\(x = -8\)[/tex] and [tex]\(y = 0\)[/tex].
- Check if [tex]\(y = 7\)[/tex]: 0 is not equal to 7.
- Conclusion: [tex]\((-8, 0)\)[/tex] is not a solution to [tex]\(y = 7\)[/tex].
Summarizing these results:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{(x, y)} & \text{Yes} & \text{No} \\ \hline (6, 2) & 0 & \checkmark \\ \hline (7, -3) & 0 & \checkmark \\ \hline (-9, 7) & \checkmark & 0 \\ \hline (-8, 0) & 0 & \checkmark \\ \hline \end{array} \][/tex]
Therefore, out of the given pairs:
- [tex]\((-9, 7)\)[/tex] is a solution to [tex]\(y = 7\)[/tex].
- The pairs [tex]\((6, 2)\)[/tex], [tex]\((7, -3)\)[/tex], and [tex]\((-8, 0)\)[/tex] are not solutions to [tex]\(y = 7\)[/tex].
1. Pair: [tex]\((6, 2)\)[/tex]
- Here, [tex]\(x = 6\)[/tex] and [tex]\(y = 2\)[/tex].
- Check if [tex]\(y = 7\)[/tex]: 2 is not equal to 7.
- Conclusion: [tex]\((6, 2)\)[/tex] is not a solution to [tex]\(y = 7\)[/tex].
2. Pair: [tex]\((7, -3)\)[/tex]
- Here, [tex]\(x = 7\)[/tex] and [tex]\(y = -3\)[/tex].
- Check if [tex]\(y = 7\)[/tex]: -3 is not equal to 7.
- Conclusion: [tex]\((7, -3)\)[/tex] is not a solution to [tex]\(y = 7\)[/tex].
3. Pair: [tex]\((-9, 7)\)[/tex]
- Here, [tex]\(x = -9\)[/tex] and [tex]\(y = 7\)[/tex].
- Check if [tex]\(y = 7\)[/tex]: 7 is equal to 7.
- Conclusion: [tex]\((-9, 7)\)[/tex] is a solution to [tex]\(y = 7\)[/tex].
4. Pair: [tex]\((-8, 0)\)[/tex]
- Here, [tex]\(x = -8\)[/tex] and [tex]\(y = 0\)[/tex].
- Check if [tex]\(y = 7\)[/tex]: 0 is not equal to 7.
- Conclusion: [tex]\((-8, 0)\)[/tex] is not a solution to [tex]\(y = 7\)[/tex].
Summarizing these results:
[tex]\[ \begin{array}{|c|c|c|} \hline \text{(x, y)} & \text{Yes} & \text{No} \\ \hline (6, 2) & 0 & \checkmark \\ \hline (7, -3) & 0 & \checkmark \\ \hline (-9, 7) & \checkmark & 0 \\ \hline (-8, 0) & 0 & \checkmark \\ \hline \end{array} \][/tex]
Therefore, out of the given pairs:
- [tex]\((-9, 7)\)[/tex] is a solution to [tex]\(y = 7\)[/tex].
- The pairs [tex]\((6, 2)\)[/tex], [tex]\((7, -3)\)[/tex], and [tex]\((-8, 0)\)[/tex] are not solutions to [tex]\(y = 7\)[/tex].
