https://file.aiquickdraw.com/mathbot/file/1726754360808ngs170sy.jpg

To solve and graph the system of inequalities:

1. \( y > 4x + 5 \)
2. \( y \geq -2x - 9 \)

Let's determine the plot points for each line.

### 1. \( y > 4x + 5 \)

The equation of the boundary line is \( y = 4x + 5 \). We need to plot points for this line:

- For \( x = 0 \): 
  \( y = 4(0) + 5 = 5 \) → \( (0, 5) \)
  
- For \( x = 1 \):
  \( y = 4(1) + 5 = 9 \) → \( (1, 9) \)
  
- For \( x = -1 \):
  \( y = 4(-1) + 5 = 1 \) → \( (-1, 1) \)

So, the points for the first inequality are \( (0, 5), (1, 9), (-1, 1) \). The region above this line will be shaded.

### 2. \( y \geq -2x - 9 \)

The equation of the boundary line is \( y = -2x - 9 \). Plot points for this line:

- For \( x = 0 \):
  \( y = -2(0) - 9 = -9 \) → \( (0, -9) \)
  
- For \( x = 1 \):
  \( y = -2(1) - 9 = -11 \) → \( (1, -11) \)
  
- For \( x = -1 \):
  \( y = -2(-1) - 9 = -7 \) → \( (-1, -7) \)

So, the points for the second inequality are \( (0, -9), (1, -11), (-1, -7) \). The region on or above this line will be shaded.

### Graphing Tips:
1. Plot the points from both inequalities.
2. Use dashed lines for \( y > 4x + 5 \) since the inequality is strict.
3. Use a solid line for \( y \geq -2x - 9 \) since the inequality includes equality.
4. Shade the region where the two conditions overlap (above both lines).

Do you need more details or help graphing? Here are some follow-up questions:

1. How do you determine if the lines are dashed or solid for inequalities?
2. How do you test which region to shade for each inequality?
3. How can you check if a specific point lies in the solution region?
4. How do you graph inequalities on the coordinate plane?
5. What are some real-world applications of solving systems of inequalities?

**Tip:** Always test a point, like \( (0, 0) \), to verify the shaded region when graphing inequalities.

Graph the solution to the system of inequalities: y > 4x + 5, y >= -2x - 9

Learn how to solve and graph the system of inequalities y > 4x + 5 and y >= -2x - 9. This problem covers key algebraic concepts such as graphing linear inequalities and determining shaded regions. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation