Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

Which ordered pairs make both inequalities true? Check all that apply.

A. (-5, 5)
B. (0, 3)
C. (0, -2)
D. (1, 1)
E. (3, -4)

Sagot :

GinnyAnswer
To determine which ordered pairs satisfy both given inequalities, let's analyze each pair step-by-step.

### Inequalities:
1. [tex]\( x + y > 0 \)[/tex]
2. [tex]\( x - y < 5 \)[/tex]

Let's check each ordered pair against these inequalities.

#### Ordered Pair: [tex]\((-5, 5)\)[/tex]
1. [tex]\( x + y = -5 + 5 = 0 \)[/tex] (This does NOT satisfy [tex]\( x + y > 0 \)[/tex])
2. [tex]\( x - y = -5 - 5 = -10 \)[/tex] (This satisfies [tex]\( x - y < 5 \)[/tex])

This pair does not satisfy the first inequality.

#### Ordered Pair: [tex]\((0, 3)\)[/tex]
1. [tex]\( x + y = 0 + 3 = 3 \)[/tex] (This satisfies [tex]\( x + y > 0 \)[/tex])
2. [tex]\( x - y = 0 - 3 = -3 \)[/tex] (This satisfies [tex]\( x - y < 5 \)[/tex])

This pair satisfies both inequalities.

#### Ordered Pair: [tex]\((0, -2)\)[/tex]
1. [tex]\( x + y = 0 - 2 = -2 \)[/tex] (This does NOT satisfy [tex]\( x + y > 0 \)[/tex])
2. [tex]\( x - y = 0 - (-2) = 2 \)[/tex] (This satisfies [tex]\( x - y < 5 \)[/tex])

This pair does not satisfy the first inequality.

#### Ordered Pair: [tex]\((1, 1)\)[/tex]
1. [tex]\( x + y = 1 + 1 = 2 \)[/tex] (This satisfies [tex]\( x + y > 0 \)[/tex])
2. [tex]\( x - y = 1 - 1 = 0 \)[/tex] (This satisfies [tex]\( x - y < 5 \)[/tex])

This pair satisfies both inequalities.

#### Ordered Pair: [tex]\((3, -4)\)[/tex]
1. [tex]\( x + y = 3 - 4 = -1 \)[/tex] (This does NOT satisfy [tex]\( x + y > 0 \)[/tex])
2. [tex]\( x - y = 3 - (-4) = 7 \)[/tex] (This does NOT satisfy [tex]\( x - y < 5 \)[/tex])

This pair does not satisfy either inequality.

### Conclusion
From the pairs checked, the ordered pairs that make both inequalities true are:
- [tex]\((0, 3)\)[/tex]
- [tex]\((1, 1)\)[/tex]

Thus, the ordered pairs [tex]\((0, 3)\)[/tex] and [tex]\((1, 1)\)[/tex] are the ones that satisfy both given inequalities.
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.