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Sagot :
Let's examine the given ordered pair [tex]\((-3, 5)\)[/tex] to determine if it satisfies the two inequalities provided:
1. The first inequality is:
[tex]\[ 2x + y > 1 \][/tex]
2. The second inequality is:
[tex]\[ x - y < 4 \][/tex]
### Step-by-Step Solution
#### Evaluating the First Inequality
First, substitute [tex]\(x = -3\)[/tex] and [tex]\(y = 5\)[/tex] into the first inequality:
[tex]\[ 2(-3) + 5 > 1 \][/tex]
This simplifies to:
[tex]\[ -6 + 5 > 1 \][/tex]
Further simplifying:
[tex]\[ -1 > 1 \][/tex]
This inequality is false.
#### Evaluating the Second Inequality
Next, substitute [tex]\(x = -3\)[/tex] and [tex]\(y = 5\)[/tex] into the second inequality:
[tex]\[ -3 - 5 < 4 \][/tex]
This simplifies to:
[tex]\[ -8 < 4 \][/tex]
This inequality is true.
### Conclusion
For the ordered pair [tex]\((-3, 5)\)[/tex]:
- The first inequality [tex]\(2x + y > 1\)[/tex] is false.
- The second inequality [tex]\(x - y < 4\)[/tex] is true.
Since both inequalities need to be true for the ordered pair to satisfy them, and we found that the first inequality is false, the ordered pair [tex]\((-3, 5)\)[/tex] does not make both inequalities true.
Therefore, the ordered pair [tex]\((-3, 5)\)[/tex] does not satisfy both inequalities.
1. The first inequality is:
[tex]\[ 2x + y > 1 \][/tex]
2. The second inequality is:
[tex]\[ x - y < 4 \][/tex]
### Step-by-Step Solution
#### Evaluating the First Inequality
First, substitute [tex]\(x = -3\)[/tex] and [tex]\(y = 5\)[/tex] into the first inequality:
[tex]\[ 2(-3) + 5 > 1 \][/tex]
This simplifies to:
[tex]\[ -6 + 5 > 1 \][/tex]
Further simplifying:
[tex]\[ -1 > 1 \][/tex]
This inequality is false.
#### Evaluating the Second Inequality
Next, substitute [tex]\(x = -3\)[/tex] and [tex]\(y = 5\)[/tex] into the second inequality:
[tex]\[ -3 - 5 < 4 \][/tex]
This simplifies to:
[tex]\[ -8 < 4 \][/tex]
This inequality is true.
### Conclusion
For the ordered pair [tex]\((-3, 5)\)[/tex]:
- The first inequality [tex]\(2x + y > 1\)[/tex] is false.
- The second inequality [tex]\(x - y < 4\)[/tex] is true.
Since both inequalities need to be true for the ordered pair to satisfy them, and we found that the first inequality is false, the ordered pair [tex]\((-3, 5)\)[/tex] does not make both inequalities true.
Therefore, the ordered pair [tex]\((-3, 5)\)[/tex] does not satisfy both inequalities.
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