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Which ordered pair makes both inequalities true?

[tex]\[
\begin{array}{l}
y \leq -x + 1 \\
y \ \textgreater \ x
\end{array}
\][/tex]

A. \((-3, 5)\)
B. \((0, 1)\)
C. \((1, -1)\)
D. [tex]\((2, 2)\)[/tex]


Sagot :

To determine whether the ordered pair \((-3, 5)\) satisfies both inequalities, we need to check it step by step for each inequality.

### Step 1: Check the first inequality
We start with the inequality \( y \leq -x + 1 \).

1. Substitute \( x = -3 \) and \( y = 5 \) into the inequality:

[tex]\[ y \leq -(-3) + 1 \][/tex]

2. Simplify the expression inside the inequality:

[tex]\[ 5 \leq 3 + 1 \][/tex]

3. Perform the addition on the right side:

[tex]\[ 5 \leq 4 \][/tex]

4. Evaluate the inequality:

[tex]\[ 5 \leq 4 \][/tex]

Clearly, \( 5 \leq 4 \) is false.

### Step 2: Check the second inequality
Now, we examine the inequality \( y > x \).

1. Substitute \( x = -3 \) and \( y = 5 \) into the inequality:

[tex]\[ 5 > -3 \][/tex]

2. Evaluate the inequality:

[tex]\[ 5 > -3 \][/tex]

This statement is true.

### Conclusion
The ordered pair \((-3, 5)\) needs to satisfy both inequalities simultaneously. From our evaluations:

- The first inequality \( y \leq -x + 1 \) evaluates to false.
- The second inequality \( y > x \) evaluates to true.

Since both conditions must be met for the pair to be a valid solution and the first condition is false, the ordered pair [tex]\((-3, 5)\)[/tex] does not make both inequalities true.