To determine which ordered pairs are solutions to the inequality [tex]\(y > \frac{1}{2} x + 5\)[/tex], we need to check each pair one by one.
1. Evaluate the pair (10, 9):
[tex]\[
y = 9, \quad x = 10
\][/tex]
Substitute [tex]\(x\)[/tex] into the expression on the right-hand side:
[tex]\[
\frac{1}{2} \cdot 10 + 5 = 5 + 5 = 10
\][/tex]
Compare [tex]\(y\)[/tex] with the result:
[tex]\[
9 > 10 \quad \text{(False)}
\][/tex]
2. Evaluate the pair (8, 10):
[tex]\[
y = 10, \quad x = 8
\][/tex]
Substitute [tex]\(x\)[/tex] into the expression on the right-hand side:
[tex]\[
\frac{1}{2} \cdot 8 + 5 = 4 + 5 = 9
\][/tex]
Compare [tex]\(y\)[/tex] with the result:
[tex]\[
10 > 9 \quad \text{(True)}
\][/tex]
3. Evaluate the pair (4, 6):
[tex]\[
y = 6, \quad x = 4
\][/tex]
Substitute [tex]\(x\)[/tex] into the expression on the right-hand side:
[tex]\[
\frac{1}{2} \cdot 4 + 5 = 2 + 5 = 7
\][/tex]
Compare [tex]\(y\)[/tex] with the result:
[tex]\[
6 > 7 \quad \text{(False)}
\][/tex]
4. Evaluate the pair (2, 6):
[tex]\[
y = 6, \quad x = 2
\][/tex]
Substitute [tex]\(x\)[/tex] into the expression on the right-hand side:
[tex]\[
\frac{1}{2} \cdot 2 + 5 = 1 + 5 = 6
\][/tex]
Compare [tex]\(y\)[/tex] with the result:
[tex]\[
6 > 6 \quad \text{(False)}
\][/tex]
Based on our evaluation, the only ordered pair that satisfies the inequality [tex]\(y > \frac{1}{2} x + 5\)[/tex] is [tex]\((8, 10)\)[/tex]. Therefore, the answer is:
[tex]\[
(8, 10)
\][/tex]
