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: -7y < -14, > 2, бх + 4y < 62, Зх — Зу 2 -9 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:
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: -7y < -14, > 2, бх + 4y < 62, Зх — Зу 2 -9 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:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please show how to solve for the corner points and how to find the feasible region when graphing the inequalities or equations. If elimination is used to solve for the corner points please show that as well.
![**Instructions for Solving a System of Linear Inequalities**
**Problem Statement:**
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. \(-7y \leq -14\)
2. \(x \geq 2\)
3. \(6x + 4y \leq 62\)
4. \(3x - 3y \geq -9\)
**Choice Question:**
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:**
[Input box for selecting an answer]
---
**Detailed Graphing Instructions:**
- **Equation 1:** \(-7y \leq -14\) simplifies to \(y \geq 2\). Draw a horizontal line at \(y = 2\) and shade above it.
- **Equation 2:** \(x \geq 2\). Draw a vertical line at \(x = 2\) and shade to the right.
- **Equation 3:** \(6x + 4y \leq 62\) simplifies to \(y \leq \frac{-3}{2}x + \frac{31}{2}\). Graph this linear inequality and shade below the line.
- **Equation 4:** \(3x - 3y \geq -9\) simplifies to \(x \geq y - 3\). Graph this inequality and shade to the right of the line.
**Conclusion:**
Upon shading all the inequalities, identify the region where all shaded areas overlap. The vertices of this region are the corner points you are looking for. Calculate their coordinates precisely by solving the equations resulting from the intersections of boundary lines forming that region. Then, choose the correct statement above to best describe your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36a79c17-bf73-44c3-9503-d2f30f855206%2F8f3d7cc0-8bd0-4892-a423-e069c04dc8b4%2Fbeac7bi_processed.png&w=3840&q=75)
Transcribed Image Text:**Instructions for Solving a System of Linear Inequalities**
**Problem Statement:**
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. \(-7y \leq -14\)
2. \(x \geq 2\)
3. \(6x + 4y \leq 62\)
4. \(3x - 3y \geq -9\)
**Choice Question:**
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:**
[Input box for selecting an answer]
---
**Detailed Graphing Instructions:**
- **Equation 1:** \(-7y \leq -14\) simplifies to \(y \geq 2\). Draw a horizontal line at \(y = 2\) and shade above it.
- **Equation 2:** \(x \geq 2\). Draw a vertical line at \(x = 2\) and shade to the right.
- **Equation 3:** \(6x + 4y \leq 62\) simplifies to \(y \leq \frac{-3}{2}x + \frac{31}{2}\). Graph this linear inequality and shade below the line.
- **Equation 4:** \(3x - 3y \geq -9\) simplifies to \(x \geq y - 3\). Graph this inequality and shade to the right of the line.
**Conclusion:**
Upon shading all the inequalities, identify the region where all shaded areas overlap. The vertices of this region are the corner points you are looking for. Calculate their coordinates precisely by solving the equations resulting from the intersections of boundary lines forming that region. Then, choose the correct statement above to best describe your solution.
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