Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Let's analyze each given point to determine if it is a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].
### Given Points:
1. [tex]\((9, 6)\)[/tex]
2. [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex]
3. [tex]\((-5, 9)\)[/tex]
### Equation:
[tex]\[ |x-2| - y = 1 \][/tex]
#### Step-by-Step Analysis:
### (a) Point [tex]\((9, 6)\)[/tex]:
1. For [tex]\( x = 9 \)[/tex], compute [tex]\( |x-2| \)[/tex]:
[tex]\[ |9-2| = |7| = 7 \][/tex]
2. Subtract [tex]\( y \)[/tex] from the result:
[tex]\[ 7 - 6 = 1 \][/tex]
3. We found that [tex]\( |9-2| - 6 = 1 \)[/tex]. Hence, [tex]\((9, 6)\)[/tex] satisfies the equation. Therefore, [tex]\((9, 6)\)[/tex] is a solution.
### (b) Point [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex]:
1. For [tex]\( x = \frac{1}{7} \)[/tex], compute [tex]\( |x-2| \)[/tex]:
[tex]\[ \left| \frac{1}{7} - 2 \right| = \left| \frac{1}{7} - \frac{14}{7} \right| = \left| -\frac{13}{7} \right| = \frac{13}{7} \][/tex]
2. Subtract [tex]\( y \)[/tex] from the result:
[tex]\[ \frac{13}{7} - \frac{6}{7} = \frac{13-6}{7} = \frac{7}{7} = 1 \][/tex]
3. We found that [tex]\( \left| \frac{1}{7} - 2 \right| - \frac{6}{7} = 1 \)[/tex]. Hence, [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] satisfies the equation. Therefore, [tex]\((\frac{1}{7}, \frac{6}{7})\)[/tex] is a solution.
### (c) Point [tex]\((-5, 9)\)[/tex]:
1. For [tex]\( x = -5 \)[/tex], compute [tex]\( |x-2| \)[/tex]:
[tex]\[ |-5 - 2| = |-7| = 7 \][/tex]
2. Subtract [tex]\( y \)[/tex] from the result:
[tex]\[ 7 - 9 = -2 \][/tex]
3. We found that [tex]\( |-5-2| - 9 = -2 \)[/tex], which does not equal 1. Hence, [tex]\((-5, 9)\)[/tex] does not satisfy the equation. Therefore, [tex]\((-5, 9)\)[/tex] is not a solution.
### Summary:
- [tex]\((9, 6)\)[/tex] is a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].
- [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] is a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].
- [tex]\((-5, 9)\)[/tex] is not a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].
So the results are:
(a) [tex]\((9,6)\)[/tex] is a solution.
(b) [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] is a solution.
(c) [tex]\((-5,9)\)[/tex] is not a solution.
### Given Points:
1. [tex]\((9, 6)\)[/tex]
2. [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex]
3. [tex]\((-5, 9)\)[/tex]
### Equation:
[tex]\[ |x-2| - y = 1 \][/tex]
#### Step-by-Step Analysis:
### (a) Point [tex]\((9, 6)\)[/tex]:
1. For [tex]\( x = 9 \)[/tex], compute [tex]\( |x-2| \)[/tex]:
[tex]\[ |9-2| = |7| = 7 \][/tex]
2. Subtract [tex]\( y \)[/tex] from the result:
[tex]\[ 7 - 6 = 1 \][/tex]
3. We found that [tex]\( |9-2| - 6 = 1 \)[/tex]. Hence, [tex]\((9, 6)\)[/tex] satisfies the equation. Therefore, [tex]\((9, 6)\)[/tex] is a solution.
### (b) Point [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex]:
1. For [tex]\( x = \frac{1}{7} \)[/tex], compute [tex]\( |x-2| \)[/tex]:
[tex]\[ \left| \frac{1}{7} - 2 \right| = \left| \frac{1}{7} - \frac{14}{7} \right| = \left| -\frac{13}{7} \right| = \frac{13}{7} \][/tex]
2. Subtract [tex]\( y \)[/tex] from the result:
[tex]\[ \frac{13}{7} - \frac{6}{7} = \frac{13-6}{7} = \frac{7}{7} = 1 \][/tex]
3. We found that [tex]\( \left| \frac{1}{7} - 2 \right| - \frac{6}{7} = 1 \)[/tex]. Hence, [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] satisfies the equation. Therefore, [tex]\((\frac{1}{7}, \frac{6}{7})\)[/tex] is a solution.
### (c) Point [tex]\((-5, 9)\)[/tex]:
1. For [tex]\( x = -5 \)[/tex], compute [tex]\( |x-2| \)[/tex]:
[tex]\[ |-5 - 2| = |-7| = 7 \][/tex]
2. Subtract [tex]\( y \)[/tex] from the result:
[tex]\[ 7 - 9 = -2 \][/tex]
3. We found that [tex]\( |-5-2| - 9 = -2 \)[/tex], which does not equal 1. Hence, [tex]\((-5, 9)\)[/tex] does not satisfy the equation. Therefore, [tex]\((-5, 9)\)[/tex] is not a solution.
### Summary:
- [tex]\((9, 6)\)[/tex] is a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].
- [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] is a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].
- [tex]\((-5, 9)\)[/tex] is not a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].
So the results are:
(a) [tex]\((9,6)\)[/tex] is a solution.
(b) [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] is a solution.
(c) [tex]\((-5,9)\)[/tex] is not a solution.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
