Graph the solution to the following system of inequalities. **Graphing Solutions to Systems of Inequalities**To effectively graph the solution to the given system of inequalities, follow these steps:1. **Identify the inequalities:** - $ y > 2x - 5 $ - $ y \leq -5x + 2 $2. **Graph each inequality on the same coordinate plane:** **Graph $ y > 2x - 5 $:** - Start by graphing the boundary line $ y = 2x - 5 $. Since the inequality is strict ($ > $), use a dashed line to represent that points on the line are not included in the solution set. - Choose a test point not on the boundary line, typically (0,0) (if it does not lie on the boundary). - Substitute (0,0) into $ y > 2x - 5 $: $ 0 > 2(0) - 5 $ simplifies to $ 0 > -5 $, which is true. - Shade the region above the dashed line, as this is the area where the inequality holds true. **Graph $ y \leq -5x + 2 $:** - Start by graphing the boundary line $ y = -5x + 2 $. Since the inequality is less than or equal to ($ \leq $), use a solid line to indicate that points on the line are part of the solution set. - Choose a test point not on the boundary line, typically (0,0) (if it does not lie on the boundary). - Substitute (0,0) into $ y \leq -5x + 2 $: $ 0 \leq -5(0) + 2 $ simplifies to $ 0 \leq 2 $, which is true. - Shade the region below the solid line, as this is the area where the inequality holds true.3. **Identify the solution region:** The solution to the system of inequalities is the region where the shaded areas overlap. This region satisfies both $ y > 2x - 5 $ and $ y \leq -5x + 2 $.**Understanding Graph Intersection:**Use the graph to determine the intersection of the shaded regions visually. Ensure to pay attention to whether the lines are dashed or solid to correctly

Answered: Graph the solution to the following…

Math

Algebra

Graph the solution to the following system of inequalities.

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter3: Graphs And Functions

Section3.4: Graph Linear Inequalities In Two Variables

Problem 277E: Harrison works two part time jobs. One at a gas station that pays $11 an hour and the other is IT...

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Question

Graph the solution to the following system of inequalities.

**Graphing Solutions to Systems of Inequalities**

To effectively graph the solution to the given system of inequalities, follow these steps:

1. **Identify the inequalities:**
- $ y > 2x - 5 $
- $ y \leq -5x + 2 $

2. **Graph each inequality on the same coordinate plane:**

**Graph $ y > 2x - 5 $:**
- Start by graphing the boundary line $ y = 2x - 5 $. Since the inequality is strict ($ > $), use a dashed line to represent that points on the line are not included in the solution set.
- Choose a test point not on the boundary line, typically (0,0) (if it does not lie on the boundary).
- Substitute (0,0) into $ y > 2x - 5 $:
$ 0 > 2(0) - 5 $ simplifies to $ 0 > -5 $, which is true.
- Shade the region above the dashed line, as this is the area where the inequality holds true.

**Graph $ y \leq -5x + 2 $:**
- Start by graphing the boundary line $ y = -5x + 2 $. Since the inequality is less than or equal to ($ \leq $), use a solid line to indicate that points on the line are part of the solution set.
- Choose a test point not on the boundary line, typically (0,0) (if it does not lie on the boundary).
- Substitute (0,0) into $ y \leq -5x + 2 $:
$ 0 \leq -5(0) + 2 $ simplifies to $ 0 \leq 2 $, which is true.
- Shade the region below the solid line, as this is the area where the inequality holds true.

3. **Identify the solution region:**
The solution to the system of inequalities is the region where the shaded areas overlap. This region satisfies both $ y > 2x - 5 $ and $ y \leq -5x + 2 $.

**Understanding Graph Intersection:**

Use the graph to determine the intersection of the shaded regions visually. Ensure to pay attention to whether the lines are dashed or solid to correctly

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