Answer
Please see the graph.
Work Step by Step
Red graph: $3x\ge y$
Blue graph: $x+2y\le8$
To determine the solutions of the system, we need to pick a point and determine if that point is a solution for each graph. We pick $(1,1)$ for both graphs.
$(1,1)$
Red graph: $3x\ge y$
$3*1\ge 1$
$3 \ge 1$ (true)
Since this is true, we shade the side of the line with the point.
$(1,1)$
Blue graph: $x+2y\le8$
$1+2*1\le8$
$1+2 \le 8$
$3 \le 8$ (true)
Since this is true, we shade the side of the line with the point.
The solution of the graph is the overlap of the two graphs.