To determine the ordered pair [tex]\((x, y)\)[/tex] that satisfies both inequalities:
[tex]\[
\begin{array}{l}
y \leq -x + 1, \\
y > x,
\end{array}
\][/tex]
let's analyze and check for the point that meets these conditions.
1. Inequality 1: [tex]\(y \leq -x + 1\)[/tex]
2. Inequality 2: [tex]\(y > x\)[/tex]
By graphing or testing different pairs, let’s verify which ordered pair satisfies both inequalities.
Let's test a few candidate points to see if they meet both criteria:
- Point [tex]\((-1, 0)\)[/tex]:
- For [tex]\(y \leq -x + 1\)[/tex]:
[tex]\[
0 \leq -(-1) + 1 \quad \text{or} \quad 0 \leq 2 \quad \text{(True)}
\][/tex]
- For [tex]\(y > x\)[/tex]:
[tex]\[
0 > -1 \quad \text{(True)}
\][/tex]
Since [tex]\((-1, 0)\)[/tex] satisfies both inequalities, it is the ordered pair that makes both inequalities true.
Thus, the ordered pair [tex]\((x, y)\)[/tex] that satisfies the given inequalities is:
[tex]\[
(-1, 0).
\][/tex]
