Let's analyze the system of inequalities step by step:

1. \( X < -3 \)
   - This tells us that the value of \( X \) must be less than \(-3\).

2. \( Y \geq 0 \)
   - This tells us that \( Y \) must be greater than or equal to 0.

3. \( Y \leq 2X + 1 \)
   - This inequality shows that \( Y \) is bounded above by the line \( Y = 2X + 1 \).

### Graphical Interpretation:
- The first inequality restricts the \( X \)-values to be less than \(-3\), so we only consider the region left of \( X = -3 \).
- The second inequality restricts the \( Y \)-values to be greater than or equal to 0, so we consider the region above the line \( Y = 0 \).
- The third inequality restricts \( Y \) to be less than or equal to the line \( Y = 2X + 1 \), which is a line with a slope of 2 and a y-intercept of 1.

The solution region is where all these conditions overlap.

Would you like a graphical solution or further explanation of these inequalities?

Here are 5 related questions to explore:
1. What happens to the system if \( X \geq -3 \) is used instead?
2. How does changing the slope in \( Y \leq 2X + 1 \) affect the solution?
3. What are the boundary points where these inequalities intersect?
4. How would the solution change if \( Y > 0 \) instead of \( Y \geq 0 \)?
5. What role does the y-intercept of \( Y = 2X + 1 \) play in determining the solution region?

**Tip:** For inequalities, always consider drawing a graph to visually understand the region they define.

Explore how to solve the system of inequalities X < -3, Y >= 0, and Y <= 2X + 1 using graphical methods. Understand key algebraic concepts and inequalities, with a step-by-step breakdown. Suitable for Grades 7-9.

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