To identify the ordered pairs \((x, y)\) that satisfy both inequalities:
[tex]\[
\begin{array}{l}
y \leq -x + 1 \\
y > x
\end{array}
\][/tex]
we need to look for the pairs that make both conditions true simultaneously. Here's a structured way to find them.
1. Understand the inequalities individually:
- The first inequality \(y \leq -x + 1\) represents all points that lie on or below the line \(y = -x + 1\).
- The second inequality \(y > x\) represents all points that lie above the line \(y = x\).
2. Combine the inequalities:
- We need to find the overlapping region where points satisfy both conditions:
- Points must be below or on the line \(y = -x + 1\).
- Points must be above the line \(y = x\).
3. Pair selection:
By analyzing the result, the following pairs \((x, y)\) satisfy both inequalities:
```
[(-10, -9), (-10, -8), (-10, -7), (-10, -6), (-10, -5), (-10, -4), (-10, -3), (-10, -2), (-10, -1), (-10, 0), (-10, 1), (-10, 2), (-10, 3), (-10, 4), (-10, 5), (-10, 6), (-10, 7), (-10, 8), (-10, 9), (-10, 10), (-9, -8), (-9, -7), (-9, -6), (-9, -5), (-9, -4), (-9, -3), (-9, -2), (-9, -1), (-9, 0), (-9, 1), (-9, 2), (-9, 3), (-9, 4), (-9, 5), (-9, 6), (-9, 7), (-9, 8), (-9, 9), (-9, 10), (-8, -7), (-8, -6), (-8, -5), (-8, -4), (-8, -3), (-8, -2), (-8, -1), (-8, 0), (-8, 1), (-8, 2), (-8, 3), (-8, 4), (-8, 5), (-8, 6), (-8, 7), (-8, 8), (-8, 9), (-7, -6), (-7, -5), (-7, -4), (-7, -3), (-7, -2), (-7, -1), (-7, 0), (-7, 1), (-7, 2), (-7, 3), (-7, 4), (-7, 5), (-7, 6), (-7, 7), (-7, 8), (-6, -5), (-6, -4), (-6, -3), (-6, -2), (-6, -1), (-6, 0), (-6, 1), (-6, 2), (-6, 3), (-6, 4), (-6, 5), (-6, 6), (-6, 7), (-5, -4), (-5, -3), (-5, -2), (-5, -1), (-5, 0), (-5, 1), (-5, 2), (-5, 3), (-5, 4), (-5, 5), (-5, 6), (-4, -3), (-4, -2), (-4, -1), (-4, 0), (-4, 1), (-4, 2), (-4, 3), (-4, 4), (-4, 5), (-3, -2), (-3, -1), (-3, 0), (-3, 1), (-3, 2), (-3, 3), (-3, 4), (-2, -1), (-2, 0), (-2, 1), (-2, 2), (-2, 3), (-1, 0), (-1, 1), (-1, 2), (0, 1)]
```
4. Examples of ordered pairs that make both inequalities true:
- Here are a few specific examples:
- \((-10, -9)\)
- \((-5, 1)\)
- \((0, 1)\)
- Any point from the above set is a valid solution that meets both criteria.
Thus, the ordered pairs listed above, such as [tex]\((0, 1)\)[/tex], satisfy both inequalities [tex]\(y \leq -x + 1\)[/tex] and [tex]\(y > x\)[/tex].
