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Graph the solution set of the system of inequalities. x+y > 3 x+y< -4 Choose the correct graph below. O A. O C. x+y=-4 Q Q OB. O D. x+y=-4 No solution (Ø) Q Q

Graph the solution set of the system of inequalities. x+y > 3 x+y< -4 Choose the correct graph below. O A. O C. x+y=-4 Q Q OB. O D. x+y=-4 No solution (Ø) Q Q

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Transcription for Educational Website:** --- **Problem Statement:** Graph the solution set of the system of inequalities: 1. \( x + y > 3 \) 2. \( x + y < -4 \) **Task:** Choose the correct graph below. **Graph Options:** - **Option A:** - A coordinate plane is shown with two lines. - The line for \( x + y = 3 \) is dashed and lies above the shaded region. - The line for \( x + y = -4 \) is dashed and parallel to the first line. - The shaded region is between the two lines. - **Option B:** - The line for \( x + y = 3 \) is dashed and appears above a shaded region. - The line for \( x + y = -4 \) is dashed below a different shaded region. - There is no overlap between the shaded regions. - **Option C:** - A coordinate plane is shown with two shaded regions, but no lines appear to fully segment the regions. - The shaded areas seem to overlap, but it does not clearly meet the inequality requirements as stated. - **Option D:** - States "No solution (∅)," indicating that there is no common region that satisfies both inequalities. --- **Analysis:** - **Feasibility Check:** - It is important to observe if there exists any overlapping shaded area in the graph options, as both lines being parallel with non-overlapping shaded regions would indicate no solution. - **Expected Correct Choice:** - The correct graph should show no overlapping region because the inequalities \( x + y > 3 \) and \( x + y < -4 \) cannot be simultaneously true. Hence, the correct option would be **D: No solution (∅)**.
Transcribed Image Text:**Transcription for Educational Website:** --- **Problem Statement:** Graph the solution set of the system of inequalities: 1. \( x + y > 3 \) 2. \( x + y < -4 \) **Task:** Choose the correct graph below. **Graph Options:** - **Option A:** - A coordinate plane is shown with two lines. - The line for \( x + y = 3 \) is dashed and lies above the shaded region. - The line for \( x + y = -4 \) is dashed and parallel to the first line. - The shaded region is between the two lines. - **Option B:** - The line for \( x + y = 3 \) is dashed and appears above a shaded region. - The line for \( x + y = -4 \) is dashed below a different shaded region. - There is no overlap between the shaded regions. - **Option C:** - A coordinate plane is shown with two shaded regions, but no lines appear to fully segment the regions. - The shaded areas seem to overlap, but it does not clearly meet the inequality requirements as stated. - **Option D:** - States "No solution (∅)," indicating that there is no common region that satisfies both inequalities. --- **Analysis:** - **Feasibility Check:** - It is important to observe if there exists any overlapping shaded area in the graph options, as both lines being parallel with non-overlapping shaded regions would indicate no solution. - **Expected Correct Choice:** - The correct graph should show no overlapping region because the inequalities \( x + y > 3 \) and \( x + y < -4 \) cannot be simultaneously true. Hence, the correct option would be **D: No solution (∅)**.
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