Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question
**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.
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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.
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y is greater then f(x) then, area is upper size 

If less then, area is lower side

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