1. **State the problem:** We are given the system of inequalities: $$x + 3y \geq 6$$ $$2x - 3y > 3$$ We need to determine if the point $(2, 2)$ is a solution to this system. 2. **Check the first inequality:** Substitute $x=2$ and $y=2$ into $x + 3y \geq 6$: $$2 + 3(2) = 2 + 6 = 8$$ Since $8 \geq 6$ is true, the point satisfies the first inequality. 3. **Check the second inequality:** Substitute $x=2$ and $y=2$ into $2x - 3y > 3$: $$2(2) - 3(2) = 4 - 6 = -2$$ Since $-2 > 3$ is false, the point does not satisfy the second inequality. 4. **Conclusion:** For a point to be a solution to the system, it must satisfy both inequalities simultaneously. Since $(2, 2)$ fails the second inequality, it is **Not Solution** to the system. 5. **Graph description:** The graph would show the lines $x + 3y = 6$ and $2x - 3y = 3$ with shading representing the solution regions. The point $(2, 2)$ lies in the region satisfying the first inequality but outside the region satisfying the second. **Final answer:** $(2, 2)$ is **Not Solution** of the system.