At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Discover solutions to your questions from experienced professionals across multiple fields 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.
Sagot :
To determine which ordered pairs satisfy both of the given inequalities:
[tex]\[ \begin{array}{c} y > -3x + 4 \\ y \leq 3x - 2 \end{array} \][/tex]
Let's analyze each ordered pair individually.
1. Ordered pair [tex]\((2,1)\)[/tex]:
- Check the first inequality [tex]\(y > -3x + 4\)[/tex]:
[tex]\[ 1 > -3(2) + 4 \][/tex]
[tex]\[ 1 > -6 + 4 \][/tex]
[tex]\[ 1 > -2 \quad \text{(True)} \][/tex]
- Check the second inequality [tex]\(y \leq 3x - 2\)[/tex]:
[tex]\[ 1 \leq 3(2) - 2 \][/tex]
[tex]\[ 1 \leq 6 - 2 \][/tex]
[tex]\[ 1 \leq 4 \quad \text{(True)} \][/tex]
Both conditions are satisfied for [tex]\((2, 1)\)[/tex].
2. Ordered pair [tex]\((1, -2)\)[/tex]:
- Check the first inequality [tex]\(y > -3x + 4\)[/tex]:
[tex]\[ -2 > -3(1) + 4 \][/tex]
[tex]\[ -2 > -3 + 4 \][/tex]
[tex]\[ -2 > 1 \quad \text{(False)} \][/tex]
Since the first condition is not satisfied, there's no need to check the second condition. [tex]\((1, -2)\)[/tex] is not in the solution set.
3. Ordered pair [tex]\((0, 4)\)[/tex]:
- Check the first inequality [tex]\(y > -3x + 4\)[/tex]:
[tex]\[ 4 > -3(0) + 4 \][/tex]
[tex]\[ 4 > 0 + 4 \][/tex]
[tex]\[ 4 > 4 \quad \text{(False)} \][/tex]
Since the first condition is not satisfied, there's no need to check the second condition. [tex]\((0, 4)\)[/tex] is not in the solution set.
4. Ordered pair [tex]\((1, 3)\)[/tex]:
- Check the first inequality [tex]\(y > -3x + 4\)[/tex]:
[tex]\[ 3 > -3(1) + 4 \][/tex]
[tex]\[ 3 > -3 + 4 \][/tex]
[tex]\[ 3 > 1 \quad \text{(True)} \][/tex]
- Check the second inequality [tex]\(y \leq 3x - 2\)[/tex]:
[tex]\[ 3 \leq 3(1) - 2 \][/tex]
[tex]\[ 3 \leq 3 - 2 \][/tex]
[tex]\[ 3 \leq 1 \quad \text{(False)} \][/tex]
Since the second condition is not satisfied, [tex]\((1, 3)\)[/tex] is not in the solution set.
After analyzing all pairs, the only ordered pair that satisfies both inequalities is [tex]\((2,1)\)[/tex].
Hence, the ordered pair that is in the solution set is [tex]\( (2, 1) \)[/tex].
[tex]\[ \begin{array}{c} y > -3x + 4 \\ y \leq 3x - 2 \end{array} \][/tex]
Let's analyze each ordered pair individually.
1. Ordered pair [tex]\((2,1)\)[/tex]:
- Check the first inequality [tex]\(y > -3x + 4\)[/tex]:
[tex]\[ 1 > -3(2) + 4 \][/tex]
[tex]\[ 1 > -6 + 4 \][/tex]
[tex]\[ 1 > -2 \quad \text{(True)} \][/tex]
- Check the second inequality [tex]\(y \leq 3x - 2\)[/tex]:
[tex]\[ 1 \leq 3(2) - 2 \][/tex]
[tex]\[ 1 \leq 6 - 2 \][/tex]
[tex]\[ 1 \leq 4 \quad \text{(True)} \][/tex]
Both conditions are satisfied for [tex]\((2, 1)\)[/tex].
2. Ordered pair [tex]\((1, -2)\)[/tex]:
- Check the first inequality [tex]\(y > -3x + 4\)[/tex]:
[tex]\[ -2 > -3(1) + 4 \][/tex]
[tex]\[ -2 > -3 + 4 \][/tex]
[tex]\[ -2 > 1 \quad \text{(False)} \][/tex]
Since the first condition is not satisfied, there's no need to check the second condition. [tex]\((1, -2)\)[/tex] is not in the solution set.
3. Ordered pair [tex]\((0, 4)\)[/tex]:
- Check the first inequality [tex]\(y > -3x + 4\)[/tex]:
[tex]\[ 4 > -3(0) + 4 \][/tex]
[tex]\[ 4 > 0 + 4 \][/tex]
[tex]\[ 4 > 4 \quad \text{(False)} \][/tex]
Since the first condition is not satisfied, there's no need to check the second condition. [tex]\((0, 4)\)[/tex] is not in the solution set.
4. Ordered pair [tex]\((1, 3)\)[/tex]:
- Check the first inequality [tex]\(y > -3x + 4\)[/tex]:
[tex]\[ 3 > -3(1) + 4 \][/tex]
[tex]\[ 3 > -3 + 4 \][/tex]
[tex]\[ 3 > 1 \quad \text{(True)} \][/tex]
- Check the second inequality [tex]\(y \leq 3x - 2\)[/tex]:
[tex]\[ 3 \leq 3(1) - 2 \][/tex]
[tex]\[ 3 \leq 3 - 2 \][/tex]
[tex]\[ 3 \leq 1 \quad \text{(False)} \][/tex]
Since the second condition is not satisfied, [tex]\((1, 3)\)[/tex] is not in the solution set.
After analyzing all pairs, the only ordered pair that satisfies both inequalities is [tex]\((2,1)\)[/tex].
Hence, the ordered pair that is in the solution set is [tex]\( (2, 1) \)[/tex].
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
