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5. Graph the solution of the system of inequalitie ly>3x-4 ¡y <2x+3 A) B) 20 15- y 10- y = 2x+35- -20-15-10 20 15 y 10- 5- 01 y=3x-4 5 10 15 20 X -20-15-10 5 10 15 20 X y=2x+3 -10y=3x-4

5. Graph the solution of the system of inequalitie ly>3x-4 ¡y <2x+3 A) B) 20 15- y 10- y = 2x+35- -20-15-10 20 15 y 10- 5- 01 y=3x-4 5 10 15 20 X -20-15-10 5 10 15 20 X y=2x+3 -10y=3x-4

Advanced Engineering Mathematics
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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**Graphing the Solution of a System of Inequalities** **Problem Statement:** Graph the solution of the system of inequalities: 1. \( y > 3x - 4 \) 2. \( y < 2x + 3 \) **Graph Representations:** **A. Graph Details:** - The graph includes two lines, \( y = 3x - 4 \) and \( y = 2x + 3 \). - The line \( y = 3x - 4 \) is solid, indicating that the solution may not include the values on this line. - The line \( y = 2x + 3 \) is solid as well, indicating that the solution might not include the line itself. - The region of interest (potential solution) does not seem to be shaded in this portion, and hence doesn't show the correct solution set. **B. Graph Details:** - Shows the same two lines, \( y = 3x - 4 \) and \( y = 2x + 3 \). - The line \( y = 3x - 4 \) is dashed, indicating values on this line are not included in the solution. - The area that may satisfy both inequalities is shaded in green. - The shading represents the region where the inequality \( y > 3x - 4 \) and \( y < 2x + 3 \) both hold true. **C. Graph Details:** - Similar to the previous graphs with the lines \( y = 3x - 4 \) and \( y = 2x + 3 \). - The method of diagramming and shading might differ from B, while still aiming to identify the overlapping region where both inequalities are satisfied. - It does not clearly represent the correct solution if shading is inconsistent with the given inequalities. **Graph Interpretation:** - In graph B, the shading correctly represents the solution region where both inequalities \( y > 3x - 4 \) and \( y < 2x + 3 \) are simultaneously satisfied. - In checking solutions for systems of inequalities, look for regions where required shading overlaps, with attention to line types (dashed or solid) denoting inclusion or exclusion of boundary lines.
Transcribed Image Text:**Graphing the Solution of a System of Inequalities** **Problem Statement:** Graph the solution of the system of inequalities: 1. \( y > 3x - 4 \) 2. \( y < 2x + 3 \) **Graph Representations:** **A. Graph Details:** - The graph includes two lines, \( y = 3x - 4 \) and \( y = 2x + 3 \). - The line \( y = 3x - 4 \) is solid, indicating that the solution may not include the values on this line. - The line \( y = 2x + 3 \) is solid as well, indicating that the solution might not include the line itself. - The region of interest (potential solution) does not seem to be shaded in this portion, and hence doesn't show the correct solution set. **B. Graph Details:** - Shows the same two lines, \( y = 3x - 4 \) and \( y = 2x + 3 \). - The line \( y = 3x - 4 \) is dashed, indicating values on this line are not included in the solution. - The area that may satisfy both inequalities is shaded in green. - The shading represents the region where the inequality \( y > 3x - 4 \) and \( y < 2x + 3 \) both hold true. **C. Graph Details:** - Similar to the previous graphs with the lines \( y = 3x - 4 \) and \( y = 2x + 3 \). - The method of diagramming and shading might differ from B, while still aiming to identify the overlapping region where both inequalities are satisfied. - It does not clearly represent the correct solution if shading is inconsistent with the given inequalities. **Graph Interpretation:** - In graph B, the shading correctly represents the solution region where both inequalities \( y > 3x - 4 \) and \( y < 2x + 3 \) are simultaneously satisfied. - In checking solutions for systems of inequalities, look for regions where required shading overlaps, with attention to line types (dashed or solid) denoting inclusion or exclusion of boundary lines.
Expert Solution
Step 1

y is greater then f(x) then, area is upper size 

If less then, area is lower side

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