The first system is:
[tex]\begin{gathered} y<-3 \\ y<\frac{2}{3}x-4 \end{gathered}[/tex]
Its graph is the following:
In this graph, we can see that the purple zone is the solution of the system and point (3,-2) is not there.
The second system is:
[tex]\begin{gathered} y>-3 \\ y\ge\frac{2}{3}x-4 \end{gathered}[/tex]
Its graphs is give by
In this graph, we can note that the purple zone is the solution and point (3,-2) is in the boundary. Since the boundary is part of the solution, then the given point is contained in the solution.
The third system is:
[tex]\begin{gathered} y>-2 \\ y\le\frac{2}{3}x-4 \end{gathered}[/tex]
Its graph is the following:
From this graph, we can see that point (3,-2) is in the corner of the solution, which is the red zone. Since the corner does not belongs to the solution, then the given point is not a solution because y must be greater than -2, strictly.
In summary, the answer is option 2
