Answer :
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.
### 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.
