Answer
Please see the graph.
Work Step by Step
Red line: $3y\le x$
Blue line: $x+3y\le6$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $3y\le x$
$3*y\le x$
$3*0 \le 0$
$0\le 0$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "less than or equal to" sign, so we use a solid line.
Blue line: $x+3y\le6$
$0+3*0\le6$
$0+0\le 6$
$0 \le 6$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "less than or equal to" sign, so we use a solid line.
The solution area for the system on inequalities is the area that is shaded both blue and red.