The graph of y≤13x−2�≤13�−2 is shown on Graph A. The graph of the system y≤13x−2�≤13�−2 is shown on Graph B. The text and diagram presented illustrate the graphs of two inequalities and the comparison of their solution sets. Below is the transcription and explanation intended for an educational website.---The graph of \( y \leq \frac{1}{3}x - 2 \) is shown on Graph A. The graph of the system \( y \leq \frac{1}{3}x - 2 \) is shown on Graph B.\( y \geq -2x + 4 \)**Description of the Graphs:**- **Graph A** displays the inequality \( y \leq \frac{1}{3}x - 2 \). The area representing the solution set is shaded below the line \( y = \frac{1}{3}x - 2 \).- **Graph B** displays the system of inequalities \( y \leq \frac{1}{3}x - 2 \) and \( y \geq -2x + 4 \). The area of the overlap between these inequalities is shaded, representing the solution set for the system.**Question:**Which TWO statements are true about the graphs?- A. The origin is included in the solution set of both graphs.- B. On Graph B, the solution set contains no ordered pairs in Quadrant III.- C. The solution set shown on Graph A is larger than the solution set of Graph B.- D. \( (0, 8) \) is part of the solution set of Graph A.- E. The point \( (5, -5) \) is included in both solution sets.**Graphical Analysis:**- Graph A includes a shaded region below the line \( y = \frac{1}{3}x - 2 \).- Graph B includes a shaded region where the solutions to \( y \leq \frac{1}{3}x - 2 \) and \( y \geq -2x + 4 \) overlap.Understanding these graphs involves interpreting the line equations and examining which regions of the coordinate plane are solutions to each inequality or system of inequalities.

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The graph of y≤-2 is shown on Graph A. The graph of the system y ≤-2 is shown on Graph B. y-2x+4 Graph A Graph B Which TWO statements are true about the graphs? A. The origin is included in the solution set of both graphs. OB. On Graph B, the solution set contains no ordered pairs in Quadrant III. □ C. The solution set shown on Graph A is larger than the solution set of Graph B. □D. (0, 8) is part of the solution set of Graph A. OE. The point (5, -5) is included in both solution sets.

The graph of y≤-2 is shown on Graph A. The graph of the system y ≤-2 is shown on Graph B. y-2x+4 Graph A Graph B Which TWO statements are true about the graphs? A. The origin is included in the solution set of both graphs. OB. On Graph B, the solution set contains no ordered pairs in Quadrant III. □ C. The solution set shown on Graph A is larger than the solution set of Graph B. □D. (0, 8) is part of the solution set of Graph A. OE. The point (5, -5) is included in both solution sets.

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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Question

The graph of y≤13x−2�≤13�−2 is shown on Graph A. The graph of the system y≤13x−2�≤13�−2 is shown on Graph B.

The text and diagram presented illustrate the graphs of two inequalities and the comparison of their solution sets. Below is the transcription and explanation intended for an educational website.

---

The graph of \( y \leq \frac{1}{3}x - 2 \) is shown on Graph A. The graph of the system \( y \leq \frac{1}{3}x - 2 \) is shown on Graph B.

\( y \geq -2x + 4 \)

**Description of the Graphs:**

- **Graph A** displays the inequality \( y \leq \frac{1}{3}x - 2 \). The area representing the solution set is shaded below the line \( y = \frac{1}{3}x - 2 \).

- **Graph B** displays the system of inequalities \( y \leq \frac{1}{3}x - 2 \) and \( y \geq -2x + 4 \). The area of the overlap between these inequalities is shaded, representing the solution set for the system.

**Question:**
Which TWO statements are true about the graphs?

- A. The origin is included in the solution set of both graphs.
- B. On Graph B, the solution set contains no ordered pairs in Quadrant III.
- C. The solution set shown on Graph A is larger than the solution set of Graph B.
- D. \( (0, 8) \) is part of the solution set of Graph A.
- E. The point \( (5, -5) \) is included in both solution sets.

**Graphical Analysis:**

- Graph A includes a shaded region below the line \( y = \frac{1}{3}x - 2 \).
- Graph B includes a shaded region where the solutions to \( y \leq \frac{1}{3}x - 2 \) and \( y \geq -2x + 4 \) overlap.

Understanding these graphs involves interpreting the line equations and examining which regions of the coordinate plane are solutions to each inequality or system of inequalities.

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