Answer
Please see the graph.
Work Step by Step
Green line: $2x+y\le5$
Blue line: $x\le3$
Orange line: $x\ge0$
Purple line: $y\ge0$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Green line: $2x+y\le5$
$2x+y\le5$
$2*0+0\le 5$
$0+0\le 5$
$0 \le 5$ (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: $x\le3$
$0 \le 3$ (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.
Orange line: $y\ge0$
$y\ge0$
$0 \ge 0$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "greater than or equal" sign, so we use a solid line.
Purple line: $y\ge0$
$0\ge0$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "greater than or equal" sign, so we use a solid line.
The solution area for the system on inequalities is the area that is shaded blue, green, purple, and orange.