there must be more than 4 campers in a group during free play and the difference between the number of boys…

Explanation:

Step1: Translate first condition

The number of campers is $x + y$, and there must be more than 4 campers. So the inequality is $x + y>4$. The boundary - line $x + y = 4$ is a dashed line (since the inequality is strict), and we test a point not on the line, say $(0,0)$. Substituting into $x + y>4$ gives $0+0 = 0<4$, so the region that does not contain the origin is the solution of $x + y>4$.

Step2: Translate second condition

The difference between the number of boys $x$ and the number of girls $y$ can be no more than 5. This gives two inequalities: $x - y\leq5$ and $y - x\leq5$. The boundary - line of $x - y=5$ has the form $y=x - 5$ and the boundary - line of $y - x = 5$ has the form $y=x + 5$. These are solid lines (since the inequalities are non - strict).

Step3: Determine the solution region

The solution of the system of inequalities is the intersection of the regions that satisfy each individual inequality.

Answer:

We need to find the graph that has a dashed line for $x + y = 4$ with the region above and to the right of it (not containing the origin), and two solid lines $y=x - 5$ and $y=x + 5$ with the region between them. Without seeing the specific labels on the graphs, the correct graph is the one that satisfies these three conditions for the inequalities $x + y>4$, $x - y\leq5$ and $y - x\leq5$.