Graph the solution set of the following system of inequalities.
2 x plus 4 y
less than or equals
4
5 x plus y
less than or equals
10
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Part 1
Use the graphing tool to graph the system of inequalities.



Here is the graph of the system of inequalities:

- The blue line represents \(y \leq -\frac{1}{2}x + 1\).
- The green line represents \(y \leq -5x + 10\).
- The yellow region shows the solution set where both inequalities overlap.

Would you like more details on this graph, or do you have any further questions?

Here are five related questions to consider:
1. How do you find the solution set of a system of inequalities algebraically?
2. What happens when the inequalities are strict (i.e., without the equal sign)?
3. Can you graph inequalities with different types of slopes, such as positive or zero slopes?
4. How do you determine the boundary lines when graphing inequalities?
5. What real-world situations can be modeled by systems of inequalities?

**Tip**: When graphing systems of inequalities, always check for the correct region by testing a point in the shaded area.

Graph the solution set of the following system of inequalities. 2x + 4y ≤ 4, 5x + y ≤ 10.

Learn how to graph the solution set of the system of inequalities 2x + 4y ≤ 4 and 5x + y ≤ 10. This tutorial covers key concepts in graphing linear inequalities and finding the intersection of solution sets, suitable for students in Grades 9-11.

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