### Graphical Solution of a System of Linear Inequalities#### Objective:Determine which of the following graphs corresponds to the solution set for the system of linear inequalities:\[\begin{cases}x + 3y > 9 \\x - y \leq 3\end{cases}\]#### Options:1. **Option A**: - This graph displays two linear boundary lines, with the regions on one side of each line shaded. 2. **Option B**: - This graph illustrates two linear boundary lines, with the regions on one side of each line shaded.3. **Option C**: - This graph shows two linear boundary lines, with the regions on one side of each line shaded.4. **Option D**: - This graph demonstrates two linear boundary lines, with the regions on one side of each line shaded.#### Explanation of Graphs:Each graph consists of the following elements:- Two lines representing the boundaries defined by the equations $ x + 3y = 9 $ and $ x - y = 3 $.- The boundary line for $ x + 3y > 9 $ is dashed, indicating that the line itself does not belong to the solution set.- The region above the line $ x + 3y = 9 $ represents the inequality $ x + 3y > 9 $.- The boundary line for $ x - y \leq 3 $ is solid, indicating that the line itself is included in the solution set.- The region below the line $ x - y = 3 $ represents the inequality $ x - y \leq 3 $.- The overlapping shaded area of these two regions represents the solution set for the system of inequalities.Choose the graph that accurately represents the combined shaded region defined by both inequalities.

Answered: Which of the following is the graph of…

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Algebra

Which of the following is the graph of the solution set of the system? √x+3y>9 x-y≤ 3

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter6: Systems Of Linear Equations And Inequalities

Section: Chapter Questions

Problem 8SGR

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Question

### Graphical Solution of a System of Linear Inequalities

#### Objective:
Determine which of the following graphs corresponds to the solution set for the system of linear inequalities:

\[
\begin{cases}
x + 3y > 9 \\
x - y \leq 3
\end{cases}
\]

#### Options:

1. **Option A**:
- This graph displays two linear boundary lines, with the regions on one side of each line shaded.

2. **Option B**:
- This graph illustrates two linear boundary lines, with the regions on one side of each line shaded.

3. **Option C**:
- This graph shows two linear boundary lines, with the regions on one side of each line shaded.

4. **Option D**:
- This graph demonstrates two linear boundary lines, with the regions on one side of each line shaded.

#### Explanation of Graphs:

Each graph consists of the following elements:
- Two lines representing the boundaries defined by the equations $ x + 3y = 9 $ and $ x - y = 3 $.
- The boundary line for $ x + 3y > 9 $ is dashed, indicating that the line itself does not belong to the solution set.
- The region above the line $ x + 3y = 9 $ represents the inequality $ x + 3y > 9 $.
- The boundary line for $ x - y \leq 3 $ is solid, indicating that the line itself is included in the solution set.
- The region below the line $ x - y = 3 $ represents the inequality $ x - y \leq 3 $.
- The overlapping shaded area of these two regions represents the solution set for the system of inequalities.

Choose the graph that accurately represents the combined shaded region defined by both inequalities.

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