To determine which ordered pair makes both inequalities true, we need to check each pair against the given inequalities:
[tex]\[
\begin{cases}
y > -3x + 3 \\
y \geq 2x - 2
\end{cases}
\][/tex]
Let's test each pair one by one:
1. Pair \((1, 0)\):
- First inequality: \( y > -3x + 3 \)
[tex]\[
0 > -3(1) + 3 \rightarrow 0 > -3 + 3 \rightarrow 0 > 0
\][/tex]
This is false.
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[
0 \geq 2(1) - 2 \rightarrow 0 \geq 2 - 2 \rightarrow 0 \geq 0
\][/tex]
This is true.
Since the first inequality is false, \((1, 0)\) does not satisfy both inequalities.
2. Pair \((-1, 1)\):
- First inequality: \( y > -3x + 3 \)
[tex]\[
1 > -3(-1) + 3 \rightarrow 1 > 3 + 3 \rightarrow 1 > 6
\][/tex]
This is false.
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[
1 \geq 2(-1) - 2 \rightarrow 1 \geq -2 - 2 \rightarrow 1 \geq -4
\][/tex]
This is true.
Since the first inequality is false, \((-1, 1)\) does not satisfy both inequalities.
3. Pair \((2, 2)\):
- First inequality: \( y > -3x + 3 \)
[tex]\[
2 > -3(2) + 3 \rightarrow 2 > -6 + 3 \rightarrow 2 > -3
\][/tex]
This is true.
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[
2 \geq 2(2) - 2 \rightarrow 2 \geq 4 - 2 \rightarrow 2 \geq 2
\][/tex]
This is true.
Since both inequalities are true, \((2, 2)\) satisfies both.
Thus, the ordered pair [tex]\((2, 2)\)[/tex] is the one that makes both inequalities true.
