A system of inequalities is shown below. ### Educational Content: System of Inequalities#### Graph and ExplanationThe image depicts a coordinate plane divided into four regions, labeled as Sections A, B, C, and D. The divisions are created by two lines representing inequalities:1. **Line for $ y_1 \leq x - 2 $** - This line slopes upwards and has a y-intercept at $-2$. It divides the plane into two regions: one where $ y $ values are less than or equal to $ x - 2 $.2. **Line for $ y_2 > -3x + 5 $** - This line slopes downwards and has a y-intercept at $5$. It divides the plane into regions where $ y $ values are greater than $-3x + 5$.The intersection and shading of these regions identify the solution sets for the system of inequalities.#### Statements to Complete- Section $ \_\_\_ $ represents the solution set to the system of inequalities.- Sections $ \_\_\_ $ represent the solution set of $ y_1 \leq x - 2 $.- Sections $ \_\_\_ $ represent the solution set of $ y_2 > -3x + 5 $.- Section $ \_\_\_ $ contains no solutions of the system of inequalities.By examining the graph:- **Section A** is located above both lines, indicating it is not a solution to either inequality.- **Section B** is below the line $ y_1 = x - 2 $ and above the line $ y_2 = -3x + 5 $, suggesting it satisfies both inequalities, making it the solution to the system.- **Section C** is only below the line $ y_1 = x - 2 $.- **Section D** is below the line $ y_2 = -3x + 5 $.Fill in the appropriate sections based on these observations:- Section **B** represents the solution set to the system of inequalities.- Sections **B and C** represent the solution set of $ y_1 \leq x - 2 $.- Sections **B and D** represent the solution set of $ y_2 > -3x + 5 $.- Section **A** contains no solutions of the system of inequalities.

A graph of the system of inequalities are given.The aim is to find the region for the specified…

A system of inequalities is shown below. Section B 10 B 6 Sections Complete the following statements so that they are true. Sections Section Section ✓represents the solution set to the system of inequalities. Section Section C X 40 X X X V Section Da V represent the solution set of y₁ ≤ x − 2. ✓represent the solution set of y2 > -3x + 5. contains no solutions of the system of inequalities.

A system of inequalities is shown below. Section B 10 B 6 Sections Complete the following statements so that they are true. Sections Section Section ✓represents the solution set to the system of inequalities. Section Section C X 40 X X X V Section Da V represent the solution set of y₁ ≤ x − 2. ✓represent the solution set of y2 > -3x + 5. contains no solutions of the system of inequalities.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

A system of inequalities is shown below.

### Educational Content: System of Inequalities

#### Graph and Explanation

The image depicts a coordinate plane divided into four regions, labeled as Sections A, B, C, and D. The divisions are created by two lines representing inequalities:

1. **Line for $ y_1 \leq x - 2 $**
- This line slopes upwards and has a y-intercept at $-2$. It divides the plane into two regions: one where $ y $ values are less than or equal to $ x - 2 $.

2. **Line for $ y_2 > -3x + 5 $**
- This line slopes downwards and has a y-intercept at $5$. It divides the plane into regions where $ y $ values are greater than $-3x + 5$.

The intersection and shading of these regions identify the solution sets for the system of inequalities.

#### Statements to Complete

- Section $ \_\_\_ $ represents the solution set to the system of inequalities.
- Sections $ \_\_\_ $ represent the solution set of $ y_1 \leq x - 2 $.
- Sections $ \_\_\_ $ represent the solution set of $ y_2 > -3x + 5 $.
- Section $ \_\_\_ $ contains no solutions of the system of inequalities.

By examining the graph:

- **Section A** is located above both lines, indicating it is not a solution to either inequality.
- **Section B** is below the line $ y_1 = x - 2 $ and above the line $ y_2 = -3x + 5 $, suggesting it satisfies both inequalities, making it the solution to the system.
- **Section C** is only below the line $ y_1 = x - 2 $.
- **Section D** is below the line $ y_2 = -3x + 5 $.

Fill in the appropriate sections based on these observations:

- Section **B** represents the solution set to the system of inequalities.
- Sections **B and C** represent the solution set of $ y_1 \leq x - 2 $.
- Sections **B and D** represent the solution set of $ y_2 > -3x + 5 $.
- Section **A** contains no solutions of the system of inequalities.

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