Answer
Please see the graph.
Work Step by Step
Blue line: $y\ge0$
Orange line: $3x+y\le4$
Red line: $x\ge0$
Green line: $x\le4$
To determine what sides of the lines to shade, we use a point not on the line. We can use (0,0) for the lines.
Blue line:
$y\ge0$
$0\ge0$ (true, so we shade above the line)
Orange line:
$3x+y\le4$
$3*0+0\le4$
$0\le5$ (true, so we shade the left side of the line)
Red line:
$x\ge0$
$0\ge0$ (true, so we shade the right side of the line)
Green line:
$x\le4$
$0\le4$ (true, so we shade the left side of the line)
The solution area is the overlap of the three inequalities. In this case, the area is the triangle created at the three intersection points of $(0,0)$, $(0,5)$, and $(2.5,0)$.
