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.
