Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To determine which ordered pair \((x, y)\) satisfies both inequalities:
[tex]\[ y > -3x + 3 \][/tex]
[tex]\[ y \geq 2x - 2 \][/tex]
we need to check each pair against both inequalities.
1. Pair (1, 0):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 0 > -3(1) + 3 \rightarrow 0 > 0 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 0 \geq 2(1) - 2 \rightarrow 0 \geq 0 \][/tex] (True)
This pair does not satisfy the first inequality, so (1, 0) is not a solution.
2. Pair (-1, 1):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 1 > -3(-1) + 3 \rightarrow 1 > 6 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 1 \geq 2(-1) - 2 \rightarrow 1 \geq -4 \][/tex] (True)
This pair does not satisfy the first inequality, so (-1, 1) is not a solution.
3. Pair (2, 2):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 2 > -3(2) + 3 \rightarrow 2 > -3 \][/tex] (True)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 2 \geq 2(2) - 2 \rightarrow 2 \geq 2 \][/tex] (True)
This pair satisfies both inequalities, so (2, 2) is a solution.
4. Pair (0, 3):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 3 > -3(0) + 3 \rightarrow 3 > 3 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 3 \geq 2(0) - 2 \rightarrow 3 \geq -2 \][/tex] (True)
This pair does not satisfy the first inequality, so (0, 3) is not a solution.
Thus, the ordered pair [tex]\((2, 2)\)[/tex] makes both inequalities true.
[tex]\[ y > -3x + 3 \][/tex]
[tex]\[ y \geq 2x - 2 \][/tex]
we need to check each pair against both inequalities.
1. Pair (1, 0):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 0 > -3(1) + 3 \rightarrow 0 > 0 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 0 \geq 2(1) - 2 \rightarrow 0 \geq 0 \][/tex] (True)
This pair does not satisfy the first inequality, so (1, 0) is not a solution.
2. Pair (-1, 1):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 1 > -3(-1) + 3 \rightarrow 1 > 6 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 1 \geq 2(-1) - 2 \rightarrow 1 \geq -4 \][/tex] (True)
This pair does not satisfy the first inequality, so (-1, 1) is not a solution.
3. Pair (2, 2):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 2 > -3(2) + 3 \rightarrow 2 > -3 \][/tex] (True)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 2 \geq 2(2) - 2 \rightarrow 2 \geq 2 \][/tex] (True)
This pair satisfies both inequalities, so (2, 2) is a solution.
4. Pair (0, 3):
- First inequality: \( y > -3x + 3 \)
[tex]\[ 3 > -3(0) + 3 \rightarrow 3 > 3 \][/tex] (False)
- Second inequality: \( y \geq 2x - 2 \)
[tex]\[ 3 \geq 2(0) - 2 \rightarrow 3 \geq -2 \][/tex] (True)
This pair does not satisfy the first inequality, so (0, 3) is not a solution.
Thus, the ordered pair [tex]\((2, 2)\)[/tex] makes both inequalities true.
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.