To solve the system of inequalities graphically, we first rewrite the system in a form suitable for graphing. Here are the inequalities provided:

1. $0x + 0y \leq 3$ — This inequality doesn't affect the region since it is trivially satisfied.
2. $0x + 2y \leq 4$, which simplifies to $y \leq 2$.
3. $x \geq 0$ — This inequality restricts the solution to the region where $x$ is non-negative (right side of the y-axis).
4. $y \geq 0$ — This restricts the solution to the region where $y$ is non-negative (above the x-axis).

Steps to Graph the System of Inequalities:

1. Inequality 1: $y \leq 2$

   • This is a horizontal line at $y = 2$. The region below or on this line (where $y$ is less than or equal to 2) is part of the solution.

2. Inequality 2: $x \geq 0$

   • This restricts the solution to the region where $x \geq 0$, which is the right half-plane (to the right of the y-axis).

3. Inequality 3: $y \geq 0$

   • This restricts the solution to the region where $y \geq 0$, which is the upper half-plane (above the x-axis).

Graphical Interpretation:

The solution region will be a triangular area bounded by the following:

• The horizontal line $y = 2$,
• The y-axis $x = 0$,
• The x-axis $y = 0$.

Corner Points:

The corner points of the solution region are:

1. $(0, 0)$ — where the x-axis and y-axis meet.
2. $(2, 0)$ — where the line $y = 2$ intersects the x-axis.
3. $(0, 2)$ — where the line $y = 2$ intersects the y-axis.

Bounded or Unbounded:

The region is bounded because it is enclosed on all sides by the x-axis, the y-axis, and the line $y = 2$.

Graphing Summary:

• The region of interest is a triangle with vertices at $(0, 0)$, $(2, 0)$, and $(0, 2)$.
• This region is bounded.

Let me know if you'd like a detailed graphical representation.

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Do you want any more details or have questions?
Here are 5 related questions to expand on the topic:

1. How do we identify if a region is bounded or unbounded?
2. How do corner points help in solving systems of inequalities graphically?
3. What would change if the inequality were $y \geq 2$ instead of $y \leq 2$?
4. Can the graphical method be applied to non-linear inequalities?
5. How do we find the feasible region in a system with more than two variables?

Tip: Always label the axes and the inequality lines when graphing, as it helps in visualizing the solution region easily.