Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Given the system of inequalities:
[tex]\[
\begin{array}{l}
y \leq -x + 1 \\
y \ \textgreater \ x
\end{array}
\][/tex]

Determine which of the following points satisfy both inequalities:
A. [tex]$(-3, 5)$[/tex]
B. [tex]$(-2, 2)$[/tex]
C. [tex]$(-1, -3)$[/tex]
D. [tex]$(0, -1)$[/tex]

Sagot :

GinnyAnswer
Sure, let's go through the conditions and check each of the given points step by step.

We need to verify each point ([tex]\( x, y \)[/tex]) against the following conditions:

1. [tex]\( y \leq -x + 1 \)[/tex]
2. [tex]\( y > x \)[/tex]

Let's evaluate each point:

1. Point [tex]\((-3, 5)\)[/tex]

- Check if [tex]\( 5 \leq -(-3) + 1 \)[/tex]
- Calculation: [tex]\( 5 \leq 3 + 1 \)[/tex]
- Simplifies to: [tex]\( 5 \leq 4 \)[/tex] (False)
- Check if [tex]\( 5 > -3 \)[/tex]
- Calculation: [tex]\( 5 > -3 \)[/tex] (True)

While [tex]\( y > x \)[/tex] is true, [tex]\( y \leq -x + 1 \)[/tex] is false. So, this point does not satisfy both conditions.

2. Point [tex]\((-2, 2)\)[/tex]

- Check if [tex]\( 2 \leq -(-2) + 1 \)[/tex]
- Calculation: [tex]\( 2 \leq 2 + 1 \)[/tex]
- Simplifies to: [tex]\( 2 \leq 3 \)[/tex] (True)
- Check if [tex]\( 2 > -2 \)[/tex]
- Calculation: [tex]\( 2 > -2 \)[/tex] (True)

Both conditions are true for this point. So, it satisfies both conditions.

3. Point [tex]\((-1, -3)\)[/tex]

- Check if [tex]\( -3 \leq -(-1) + 1 \)[/tex]
- Calculation: [tex]\( -3 \leq 1 + 1 \)[/tex]
- Simplifies to: [tex]\( -3 \leq 2 \)[/tex] (True)
- Check if [tex]\( -3 > -1 \)[/tex]
- Calculation: [tex]\( -3 > -1 \)[/tex] (False)

While [tex]\( y \leq -x + 1 \)[/tex] is true, [tex]\( y > x \)[/tex] is false. So, this point does not satisfy both conditions.

4. Point [tex]\((0, -1)\)[/tex]

- Check if [tex]\( -1 \leq -(0) + 1 \)[/tex]
- Calculation: [tex]\( -1 \leq 0 + 1 \)[/tex]
- Simplifies to: [tex]\( -1 \leq 1 \)[/tex] (True)
- Check if [tex]\( -1 > 0 \)[/tex]
- Calculation: [tex]\( -1 > 0 \)[/tex] (False)

While [tex]\( y \leq -x + 1 \)[/tex] is true, [tex]\( y > x \)[/tex] is false. So, this point does not satisfy both conditions.

After examining all the points, we find that the only point that meets both conditions is [tex]\((-2, 2)\)[/tex].

So the valid point is:
[tex]\[ [(-2, 2)] \][/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.