To determine which ordered pairs make both inequalities true, we need to analyze and test each given pair against the two inequalities:
[tex]\[
\begin{array}{l}
y > -2x + 3 \\
y \leq x - 2
\end{array}
\][/tex]
1. Testing the pair [tex]\((0, 0)\)[/tex]:
- For the first inequality:
[tex]\[
y > -2x + 3 \implies 0 > -2(0) + 3 \implies 0 > 3
\][/tex]
This is not true. So, [tex]\((0, 0)\)[/tex] does not satisfy the first inequality.
2. Testing the pair [tex]\((0, -1)\)[/tex]:
- For the first inequality:
[tex]\[
y > -2x + 3 \implies -1 > -2(0) + 3 \implies -1 > 3
\][/tex]
This is not true. So, [tex]\((0, -1)\)[/tex] does not satisfy the first inequality.
3. Testing the pair [tex]\((1, 1)\)[/tex]:
- For the first inequality:
[tex]\[
y > -2x + 3 \implies 1 > -2(1) + 3 \implies 1 > -2 + 3 \implies 1 > 1
\][/tex]
This is not true. So, [tex]\((1, 1)\)[/tex] does not satisfy the first inequality.
Since none of the given pairs satisfy the first inequality, we can conclude that no ordered pairs make both inequalities true.
Thus, the set of valid points is:
[tex]\[
[]
\][/tex]
No ordered pairs from the given options satisfy both inequalities simultaneously.
