To determine which point is in the solution set of this system of inequalities, we need to test each given point against the two inequalities:

1. $y < -2x + 1$
2. $x + 2y \geq -4$

Test Point A: $(-9, 1)$

• For $y < -2x + 1$: $1 < -2(-9) + 1$ $1 < 18 + 1$ $1 < 19 \quad \text{(True)}$
• For $x + 2y \geq -4$: $-9 + 2(1) \geq -4$ $-9 + 2 \geq -4$ $-7 \geq -4 \quad \text{(False)}$ Thus, point A does not satisfy both inequalities.

Test Point B: $(-5, 4)$

• For $y < -2x + 1$: $4 < -2(-5) + 1$ $4 < 10 + 1$ $4 < 11 \quad \text{(True)}$
• For $x + 2y \geq -4$: $-5 + 2(4) \geq -4$ $-5 + 8 \geq -4$ $3 \geq -4 \quad \text{(True)}$ Thus, point B satisfies both inequalities.

Test Point C: $(2, -3)$

• For $y < -2x + 1$: $-3 < -2(2) + 1$ $-3 < -4 + 1$ $-3 < -3 \quad \text{(False, because -3 is not less than -3)}$ Thus, point C does not satisfy the first inequality.

Test Point D: $(6, -8)$

• For $y < -2x + 1$: $-8 < -2(6) + 1$ $-8 < -12 + 1$ $-8 < -11 \quad \text{(False)}$ Thus, point D does not satisfy the first inequality.

Conclusion:

The only point that satisfies both inequalities is B: $(-5, 4)$.

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Do you need further explanation or any additional details? Here are five related questions to expand your understanding:

1. How do you graph systems of inequalities on a coordinate plane?
2. How would the solution set look visually for this system?
3. How can you determine if a system of inequalities has no solution?
4. What happens if both inequalities have the same slope?
5. Can inequalities with different variables (like $x$ and $y$) be solved similarly?

Tip: When testing a point in an inequality, plug the coordinates into both inequalities and check for consistency with the inequality signs.