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
![**Title: Solving Systems of Inequalities - Graphical Representation**
**Explanation:**
The task given is to find a system of inequalities using the provided graph.
**Graph Description:**
1. **Grid Layout:**
The graph is on a Cartesian plane with the x-axis and y-axis both ranging from -5 to 5.
2. **Key Features:**
- **Vertical Line:** There is a vertical dashed blue line intersecting the x-axis at \( x = 0 \). The dashed nature of the line indicates that the inequality associated with it is either \( x \leq 0 \) or \( x \geq 0 \), but the boundary itself (i.e., \( x = 0 \)) is not included in the solution set.
- **Horizontal Line:** There is a horizontal dashed red line intersecting the y-axis at \( y = -5 \). The dashed nature of this line suggests that the inequality associated with it might be either \( y \leq -5 \) or \( y \geq -5 \), but the boundary itself \( y = -5 \) is not included in the solution set.
3. **Shaded Region:**
- The region of interest is shaded in gray, which indicates the solution set where both inequalities are true simultaneously. The shaded area covers the entire region to the left of the blue dashed line and above the red dashed line.
**System of Inequalities:**
Based on the graph:
- Since the shaded area is to the left of the line \( x = 0 \), the inequality is \( x \leq 0 \).
- Since the shaded area is above the line \( y = -5 \), the inequality is \( y \geq -5 \).
Thus, the system of inequalities represented by the graph is:
\[ x \leq 0 \]
\[ y \geq -5 \]
**Conclusion:**
When solving a system of inequalities graphically, the solution is often represented by a shaded region on the Cartesian plane. The boundaries of this shaded region are determined by the inequalities, with dashed lines indicating non-inclusive boundaries. In this case, the inequalities \( x \leq 0 \) and \( y \geq -5 \) define the shaded solution region of the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F006a35a3-e559-4cc9-aa53-746bb30a70e8%2F2d02c89f-7ede-4ff1-9e6f-abfe27c63cb3%2Fvtykzdy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Solving Systems of Inequalities - Graphical Representation**
**Explanation:**
The task given is to find a system of inequalities using the provided graph.
**Graph Description:**
1. **Grid Layout:**
The graph is on a Cartesian plane with the x-axis and y-axis both ranging from -5 to 5.
2. **Key Features:**
- **Vertical Line:** There is a vertical dashed blue line intersecting the x-axis at \( x = 0 \). The dashed nature of the line indicates that the inequality associated with it is either \( x \leq 0 \) or \( x \geq 0 \), but the boundary itself (i.e., \( x = 0 \)) is not included in the solution set.
- **Horizontal Line:** There is a horizontal dashed red line intersecting the y-axis at \( y = -5 \). The dashed nature of this line suggests that the inequality associated with it might be either \( y \leq -5 \) or \( y \geq -5 \), but the boundary itself \( y = -5 \) is not included in the solution set.
3. **Shaded Region:**
- The region of interest is shaded in gray, which indicates the solution set where both inequalities are true simultaneously. The shaded area covers the entire region to the left of the blue dashed line and above the red dashed line.
**System of Inequalities:**
Based on the graph:
- Since the shaded area is to the left of the line \( x = 0 \), the inequality is \( x \leq 0 \).
- Since the shaded area is above the line \( y = -5 \), the inequality is \( y \geq -5 \).
Thus, the system of inequalities represented by the graph is:
\[ x \leq 0 \]
\[ y \geq -5 \]
**Conclusion:**
When solving a system of inequalities graphically, the solution is often represented by a shaded region on the Cartesian plane. The boundaries of this shaded region are determined by the inequalities, with dashed lines indicating non-inclusive boundaries. In this case, the inequalities \( x \leq 0 \) and \( y \geq -5 \) define the shaded solution region of the graph.
Transcribed Image Text:**Question:**
Choose the system that matches the graph.
**Options:**
- **A.**
- \( x < 3 \)
- \( y > -3 \)
- **B.**
- \( x \leq -3 \)
- \( y > 3 \)
- **C.**
- \( x \geq -3 \)
- \( y < 3 \)
- **D.**
- \( x > 3 \)
- \( y < -3 \)
*Note: The graph or diagrams referred to in the question are not provided.*
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