Determine graphically the solution set for the system of inequalities. \[ \begin{array}{l} 2 x+4 y>16 \\ -x+3 y \geq 7 \end{array} \]

Step 1 ：First, we need to plot the two inequalities on a graph. The inequalities are \(2x + 4y > 16\) and \(-x + 3y \geq 7\).

Step 2 ：The solution set will be the region where both inequalities are satisfied. This means we are looking for the area where the red and blue areas on the graph overlap.

Step 3 ：By observing the graph, we can see the overlapping region which represents the values of x and y that satisfy both inequalities.

Step 4 ：\(\boxed{\text{The solution set for the system of inequalities is the region where the red and blue areas overlap on the graph.}}\)