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Let's analyze the inequalities presented and how to graph the first one:

The inequalities given are:

1. \( 2y < 2x + 8 \)
2. \( 5y \geq -5x - 50 \)

For Step 1, we focus on graphing the solution set of the first inequality: 

### 1. \( 2y < 2x + 8 \)
First, convert this inequality to slope-intercept form by solving for \( y \):

\[
2y = 2x + 8
\]
\[
y = x + 4
\]

So, the boundary line equation is \( y = x + 4 \). The inequality is \( 2y < 2x + 8 \), which means we will use a dashed line to represent the boundary, and the shading will be below the line since it's a "<" inequality.

### Points to plot:
We need to find two points on the line \( y = x + 4 \). Let's choose easy values of \( x \) and solve for \( y \).

- For \( x = 0 \):
  \[
  y = 0 + 4 = 4
  \]
  So, one point is \( (0, 4) \).

- For \( x = 2 \):
  \[
  y = 2 + 4 = 6
  \]
  So, another point is \( (2, 6) \).

### Now we enter the following information:
- Boundary Line: **Dashed** (since the inequality is strict "<").
- Points on the Boundary: \( (0, 4) \) and \( (2, 6) \).
- Region to Shade: **Below the line** (the inequality is "<", which means shading below).

Would you like further details or assistance with the next inequality?

Here are 5 follow-up questions:
1. How do we graph the second inequality \( 5y \geq -5x - 50 \)?
2. What changes when you have \( \geq \) or \( \leq \) inequalities compared to strict \( > \) or \( < \)?
3. How do you determine which region to shade for a system of inequalities?
4. How do you find the intersection of the two shaded regions?
5. How do we handle solutions that are outside the viewing window of the graph?

**Tip:** Always start by solving each inequality for \( y \) to make graphing easier!

Solve the system of two linear inequalities graphically: 2y < 2x + 8 or 5y ≥ -5x - 50.

Learn how to solve and graph the system of two linear inequalities: 2y < 2x + 8 and 5y ≥ -5x - 50. The solution involves understanding slope-intercept form, determining boundary lines, and identifying shaded regions to find the solution set.

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