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To graph the solution set of this system of inequalities:

1. **Rewrite the inequalities** in slope-intercept form, \( y = mx + b \), to make graphing easier.

   **Inequality 1:** \( 2x + 4y \leq 4 \)
   
   - Solve for \( y \): 
     \[
     4y \leq -2x + 4
     \]
     \[
     y \leq -\frac{1}{2}x + 1
     \]
   
   **Inequality 2:** \( 4x + y \leq 8 \)
   
   - Solve for \( y \):
     \[
     y \leq -4x + 8
     \]

2. **Graph each inequality**:
   - The first inequality \( y \leq -\frac{1}{2}x + 1 \) has a slope of \(-\frac{1}{2}\) and y-intercept \(1\). Draw the line \( y = -\frac{1}{2}x + 1 \) (solid line because of \( \leq \)), and shade below it.
   - The second inequality \( y \leq -4x + 8 \) has a slope of \(-4\) and y-intercept \(8\). Draw the line \( y = -4x + 8 \) (also solid), and shade below it.

3. **Find the intersection region**:
   - The solution set is the region where the shaded areas of both inequalities overlap. This represents all points \((x, y)\) that satisfy both inequalities simultaneously.

Would you like a detailed step-by-step on finding the intersection points or graphing tips?

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### Related Questions
1. How do we solve systems of inequalities with more than two inequalities?
2. What changes if one or both inequalities were strict inequalities (\(<\) instead of \( \leq \))?
3. How do we interpret the slope and intercept of an inequality line?
4. How can we determine if a particular point lies in the solution region?
5. How would the graph look if one inequality had a positive slope?

### Tip:
To verify your graph, test a point in the overlapping region (like \((0,0)\), if it lies in that area) to see if it satisfies both inequalities.

Graph the solution set of the following system of inequalities: 2x + 4y ≤ 4, 4x + y ≤ 8.

Learn how to graph the solution set for a system of inequalities involving 2x + 4y ≤ 4 and 4x + y ≤ 8. This solution includes rewriting inequalities in slope-intercept form, graphing linear inequalities, and finding the intersection region. Suitable for students in Grades 9-12.

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