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Which ordered pair makes both inequalities true?
[tex]\[
\begin{array}{l}
y \ \textgreater \ -2x + 3 \\
y \leq x - 2
\end{array}
\][/tex]

A. [tex]\((0, 0)\)[/tex]

B. [tex]\((0, -1)\)[/tex]

C. [tex]\((1, 1)\)[/tex]

D. [tex]\((3, 0)\)[/tex]



Answer :

GinnyAnswer
To determine which ordered pair [tex]\((x, y)\)[/tex] satisfies both inequalities, we need to check each one step by step. The inequalities are:

1. [tex]\( y > -2x + 3 \)[/tex]
2. [tex]\( y \leq x - 2 \)[/tex]

Let's test each given pair:

1. Pair [tex]\((0,0)\)[/tex]:
- Inequality 1: [tex]\( 0 > -2(0) + 3 \Rightarrow 0 > 3\)[/tex] (False)
- Since it fails the first inequality, no need to check the second one.

2. Pair [tex]\((0,-1)\)[/tex]:
- Inequality 1: [tex]\( -1 > -2(0) + 3 \Rightarrow -1 > 3\)[/tex] (False)
- Since it fails the first inequality, no need to check the second one.

3. Pair [tex]\((1,1)\)[/tex]:
- Inequality 1: [tex]\( 1 > -2(1) + 3 \Rightarrow 1 > 1\)[/tex] (False)
- Since it fails the first inequality, no need to check the second one.

4. Pair [tex]\((3,0)\)[/tex]:
- Inequality 1: [tex]\( 0 > -2(3) + 3 \Rightarrow 0 > -6 + 3 \Rightarrow 0 > -3\)[/tex] (True)
- Since it satisfies the first inequality, we check the second:
- Inequality 2: [tex]\( 0 \leq 3 - 2 \Rightarrow 0 \leq 1\)[/tex] (True)

Therefore, the ordered pair [tex]\((3, 0)\)[/tex] makes both inequalities true. The solution is:

[tex]\[ (3, 0) \][/tex]

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