Graph and shade the points (if any) that satisfy the following system of linear inequalities. Then find the coordinates of all of the corner points: 14x + 3y < 71, х — 9у > -41, 13х + 12у -17, x + 4y < 34 Which one of the following statements best describes your solution: A. There are no corner points, because there are no points that satisfy all of the inequalities. B. There are no corner points, because the shaded points constitute a single half-plane. C. There is exactly one corner point. D. There are exactly two corner points. E. There are exactly three corner points. F. There are exactly four corner points. G. There are exactly five corner points. H. There are more than five corner points. Statement: e • Part 2 Yes, that is correct. What are the corner points? Beginning with the corner point that is in the first quadrant and then proceeding around the boundary in counter-clockwise order, enter the coordinates of the corner points: What is the corner that lies in the first quadrant: ( What is the corner that lies in the second quadrant: ( What is the corner that lies in the fourth quadrant: ( 6.2 -5.3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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### Solving a System of Linear Inequalities

**Task:**  
Graph and shade the points (if any) that satisfy the following system of linear inequalities. Then find the coordinates of all of the corner points:

1. \( 14x + 3y \leq 71 \)
2. \( x - 9y \geq -41 \)
3. \( 13x + 12y \geq -17 \)
4. \( x + 4y \leq 34 \)

**Instructions:**  
Determine which one of the following statements best describes your solution:

A. There are no corner points, because there are no points that satisfy all of the inequalities.  
B. There are no corner points, because the shaded points constitute a single half-plane.  
C. There is exactly one corner point.  
D. There are exactly two corner points.  
E. There are exactly three corner points.  
F. There are exactly four corner points.  
G. There are exactly five corner points.  
H. There are more than five corner points.

**Solution:**  
The correct statement is: 
- **E. There are exactly three corner points.**

### Part 2

**Question:**  
Yes, that is correct. What are the corner points? Beginning with the corner point that is in the first quadrant and then proceeding around the boundary in counter-clockwise order, enter the coordinates of the corner points:

1. What is the corner that lies in the first quadrant: \( ( \, , \, ) \)
2. What is the corner that lies in the second quadrant: \( ( \, , \, ) \)
3. What is the corner that lies in the fourth quadrant: \( (6.2, -5.3) \)
Transcribed Image Text:### Solving a System of Linear Inequalities **Task:** Graph and shade the points (if any) that satisfy the following system of linear inequalities. Then find the coordinates of all of the corner points: 1. \( 14x + 3y \leq 71 \) 2. \( x - 9y \geq -41 \) 3. \( 13x + 12y \geq -17 \) 4. \( x + 4y \leq 34 \) **Instructions:** Determine which one of the following statements best describes your solution: A. There are no corner points, because there are no points that satisfy all of the inequalities. B. There are no corner points, because the shaded points constitute a single half-plane. C. There is exactly one corner point. D. There are exactly two corner points. E. There are exactly three corner points. F. There are exactly four corner points. G. There are exactly five corner points. H. There are more than five corner points. **Solution:** The correct statement is: - **E. There are exactly three corner points.** ### Part 2 **Question:** Yes, that is correct. What are the corner points? Beginning with the corner point that is in the first quadrant and then proceeding around the boundary in counter-clockwise order, enter the coordinates of the corner points: 1. What is the corner that lies in the first quadrant: \( ( \, , \, ) \) 2. What is the corner that lies in the second quadrant: \( ( \, , \, ) \) 3. What is the corner that lies in the fourth quadrant: \( (6.2, -5.3) \)
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