1. **State the problem:** We are given the system of inequalities: $$3x + y \geq 3$$ $$x + 2y < -4$$ We need to determine if the point $(1, -3)$ is a solution to this system. 2. **Recall the rule:** A point is a solution to a system of inequalities if it satisfies all inequalities in the system. 3. **Check the first inequality:** Substitute $x=1$ and $y=-3$ into $3x + y \geq 3$: $$3(1) + (-3) = 3 - 3 = 0$$ Check if $0 \geq 3$: This is false. 4. **Check the second inequality:** Substitute $x=1$ and $y=-3$ into $x + 2y < -4$: $$1 + 2(-3) = 1 - 6 = -5$$ Check if $-5 < -4$: This is true. 5. **Conclusion:** Since the point $(1, -3)$ does not satisfy the first inequality, it is **not a solution** to the system. 6. **Graphing note:** The first inequality $3x + y \geq 3$ represents the region above or on the line $y = -3x + 3$. The second inequality $x + 2y < -4$ represents the region below the line $y = -\frac{1}{2}x - 2$. The solution to the system is the intersection of these two regions. Since $(1, -3)$ lies below the first line (does not satisfy the first inequality), it is outside the solution region. **Final answer:** $(1, -3)$ is **Not Solution** to the system.