To solve this, we need to determine which of the given ordered pairs satisfy the inequality $-2x + 3y \geq 3$. We test each pair by substituting the values of $x$ and $y$ into the inequality.

1. Test $(-1, 2)$:

Substitute $x = -1$ and $y = 2$: $-2(-1) + 3(2) = 2 + 6 = 8$ Since $8 \geq 3$, $(-1, 2)$ is a solution.

2. Test $(0, 1)$:

Substitute $x = 0$ and $y = 1$: $-2(0) + 3(1) = 0 + 3 = 3$ Since $3 \geq 3$, $(0, 1)$ is a solution.

3. Test $(4, 1)$:

Substitute $x = 4$ and $y = 1$: $-2(4) + 3(1) = -8 + 3 = -5$ Since $-5 \not\geq 3$, $(4, 1)$ is not a solution.

4. Test $(2, 3)$:

Substitute $x = 2$ and $y = 3$: $-2(2) + 3(3) = -4 + 9 = 5$ Since $5 \geq 3$, $(2, 3)$ is a solution.

Final Answer:

The ordered pairs that are solutions are: $\boxed{(-1, 2), (0, 1), (2, 3)}$

Would you like further clarification or additional examples?
Here are 5 follow-up questions for exploration:

1. What is the difference between solving inequalities and equations?
2. How would the inequality change if it were strict ($-2x + 3y > 3$)?
3. How can you graph this inequality to visualize the solution set?
4. How does changing the coefficients of $x$ and $y$ impact the inequality?
5. What happens to the solution set if the inequality is flipped ($-2x + 3y \leq 3$)?

Tip: Always substitute values carefully and check your calculations when solving inequalities!