Answer
Please see the graph.
Work Step by Step
Red line: $x+2y\le5$
Purple line: $x\le2$
Black line: $x\ge0$
Orange line: $y\ge0$
To determine what sides of the lines to shade, we use a point not on the line. We can use (1,1) for the lines.
Red line:
$x+2y\le5$
$1+2*1\le5$
$1+2\le5$
$3\le5$ (true, so we shade the left side of the line)
Purple line:
$x\le2$
$1\le2$ (true, so we shade the left side of the line)
Black line:
$x\ge0$
$1\ge0$ (true, so we shade the right side of the line)
Orange line:
$y\ge0$
$1\ge0$ (true, so we shade above the line)
The solution area is the overlap of the four inequalities. The solution area is bounded by the four points at $(0,0)$, $(2,0)$, $(0,2.5)$, and $(2,1.5)$
