Answer :
To determine whether the ordered pair [tex]\((-3, 5)\)[/tex] satisfies both inequalities [tex]\( y \leq -x + 1 \)[/tex] and [tex]\( y > x \)[/tex], we need to check each inequality step by step.
### Checking the First Inequality: [tex]\( y \leq -x + 1 \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 5 \)[/tex] into the inequality:
[tex]\[ y \leq -x + 1 \][/tex]
becomes
[tex]\[ 5 \leq -(-3) + 1 \][/tex]
2. Simplify the right-hand side:
[tex]\[ 5 \leq 3 + 1 \][/tex]
[tex]\[ 5 \leq 4 \][/tex]
3. Determine if the inequality is true:
[tex]\[ 5 \leq 4 \quad \text{is false} \][/tex]
Since [tex]\( 5 \leq 4 \)[/tex] is false, the first inequality is not satisfied.
### Checking the Second Inequality: [tex]\( y > x \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 5 \)[/tex] into the inequality:
[tex]\[ y > x \][/tex]
becomes
[tex]\[ 5 > -3 \][/tex]
2. Determine if the inequality is true:
[tex]\[ 5 > -3 \quad \text{is true} \][/tex]
Since [tex]\( 5 > -3 \)[/tex] is true, the second inequality is satisfied.
### Conclusion:
For the ordered pair [tex]\((-3, 5)\)[/tex]:
- The first inequality [tex]\( y \leq -x + 1 \)[/tex] is false.
- The second inequality [tex]\( y > x \)[/tex] is true.
Therefore, the ordered pair [tex]\((-3, 5)\)[/tex] does not make both inequalities true simultaneously. Only one of the inequalities is satisfied.
### Checking the First Inequality: [tex]\( y \leq -x + 1 \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 5 \)[/tex] into the inequality:
[tex]\[ y \leq -x + 1 \][/tex]
becomes
[tex]\[ 5 \leq -(-3) + 1 \][/tex]
2. Simplify the right-hand side:
[tex]\[ 5 \leq 3 + 1 \][/tex]
[tex]\[ 5 \leq 4 \][/tex]
3. Determine if the inequality is true:
[tex]\[ 5 \leq 4 \quad \text{is false} \][/tex]
Since [tex]\( 5 \leq 4 \)[/tex] is false, the first inequality is not satisfied.
### Checking the Second Inequality: [tex]\( y > x \)[/tex]
1. Substitute [tex]\( x = -3 \)[/tex] and [tex]\( y = 5 \)[/tex] into the inequality:
[tex]\[ y > x \][/tex]
becomes
[tex]\[ 5 > -3 \][/tex]
2. Determine if the inequality is true:
[tex]\[ 5 > -3 \quad \text{is true} \][/tex]
Since [tex]\( 5 > -3 \)[/tex] is true, the second inequality is satisfied.
### Conclusion:
For the ordered pair [tex]\((-3, 5)\)[/tex]:
- The first inequality [tex]\( y \leq -x + 1 \)[/tex] is false.
- The second inequality [tex]\( y > x \)[/tex] is true.
Therefore, the ordered pair [tex]\((-3, 5)\)[/tex] does not make both inequalities true simultaneously. Only one of the inequalities is satisfied.