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Answer :
Certainly! Let's analyze and solve the given question step-by-step.
### Question Analysis:
We are provided with multiple choice questions about the nature of systems of linear equations in two variables and their graphs.
### Part 1: Identifying a System of Linear Equations in Two Variables:
The question asks us to identify which option represents a system of linear equations in two variables.
Let's review each option:
Option A: [tex]\(2x - 7y = 8\)[/tex]
This is a single linear equation with two variables.
Option B: [tex]\(\left\{\begin{array}{l}3x + 5y = 2 \\ x - 4y = 0\end{array}\right.\)[/tex]
This represents two linear equations in two variables, which is indeed a system of linear equations.
Option C:
[tex]\[
4x - 1 = 8 \\
x - 4y = 9
\][/tex]
These are two linear equations, but they are written separately and not in the form of a paired system.
Option D: [tex]\(\left\{\begin{array}{c}x + 9y \leq 2 \\ 2x - 3y > 12\end{array}\right.\)[/tex]
These are linear inequalities, not linear equations.
By analyzing the options, Option B is the correct choice because it represents a system of linear equations in two variables.
### Part 2: Identifying a Non-Graph of a System of Linear Equations:
Given the details provided in the question and considering the numerical result provided:
The Python solution suggests a context where:
- Initial amount of money: 23 units
- Cost per bagel: 3 units
- Number of bagels: 5
From this context:
1. Calculate the total cost for the bagels: [tex]\( 3 \times 5 = 15 \)[/tex]
2. Calculate the remaining amount of money after buying the bagels: [tex]\( 23 - 15 = 8 \)[/tex]
Based on the given numerical results, the total cost of the bagels is 15 units, and the remaining amount of money is 8 units after purchasing the bagels.
This doesn't directly relate to the graph of a system of linear equations, but it's important to understand the interpretation of the provided context correctly.
To conclude Part 2 without specific graph options provided, one would need to visually determine if any graph does not match the criteria of being a linear system when looking at potential graph choices.
### Therefore, the correct solutions are:
1. Part 1: The system of linear equations in two variables is:
- Option B: [tex]\(\left\{\begin{array}{l}3x + 5y = 2 \\ x - 4y = 0\end{array}\right.\)[/tex]
2. Part 2: Without graph options in the question, if provided, we look for the one that does not depict linear relationships.
I hope this clarifies the solution steps for the given math problem! If you have any further questions, feel free to ask.
### Question Analysis:
We are provided with multiple choice questions about the nature of systems of linear equations in two variables and their graphs.
### Part 1: Identifying a System of Linear Equations in Two Variables:
The question asks us to identify which option represents a system of linear equations in two variables.
Let's review each option:
Option A: [tex]\(2x - 7y = 8\)[/tex]
This is a single linear equation with two variables.
Option B: [tex]\(\left\{\begin{array}{l}3x + 5y = 2 \\ x - 4y = 0\end{array}\right.\)[/tex]
This represents two linear equations in two variables, which is indeed a system of linear equations.
Option C:
[tex]\[
4x - 1 = 8 \\
x - 4y = 9
\][/tex]
These are two linear equations, but they are written separately and not in the form of a paired system.
Option D: [tex]\(\left\{\begin{array}{c}x + 9y \leq 2 \\ 2x - 3y > 12\end{array}\right.\)[/tex]
These are linear inequalities, not linear equations.
By analyzing the options, Option B is the correct choice because it represents a system of linear equations in two variables.
### Part 2: Identifying a Non-Graph of a System of Linear Equations:
Given the details provided in the question and considering the numerical result provided:
The Python solution suggests a context where:
- Initial amount of money: 23 units
- Cost per bagel: 3 units
- Number of bagels: 5
From this context:
1. Calculate the total cost for the bagels: [tex]\( 3 \times 5 = 15 \)[/tex]
2. Calculate the remaining amount of money after buying the bagels: [tex]\( 23 - 15 = 8 \)[/tex]
Based on the given numerical results, the total cost of the bagels is 15 units, and the remaining amount of money is 8 units after purchasing the bagels.
This doesn't directly relate to the graph of a system of linear equations, but it's important to understand the interpretation of the provided context correctly.
To conclude Part 2 without specific graph options provided, one would need to visually determine if any graph does not match the criteria of being a linear system when looking at potential graph choices.
### Therefore, the correct solutions are:
1. Part 1: The system of linear equations in two variables is:
- Option B: [tex]\(\left\{\begin{array}{l}3x + 5y = 2 \\ x - 4y = 0\end{array}\right.\)[/tex]
2. Part 2: Without graph options in the question, if provided, we look for the one that does not depict linear relationships.
I hope this clarifies the solution steps for the given math problem! If you have any further questions, feel free to ask.
Thanks for taking the time to read PART III SUMMATIVE EVALUATION Read each item carefully and write the correct answer on the blank provided before the number I Multiple Choice Directions Select. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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