Answer
Please see the graph.
Work Step by Step
Orange line: $2y-x\ge1$
Blue line: $x+y\ge-4$
Red line: $y\le2$
To determine what side of the lines to shade, we use a point not on any of the lines (such as the origin, (0,0)).
Orange line:
$2y-x\ge1$
$2*0-0\ge1$
$0-0\ge1$
$0\ge1$ (false, so we shade the left side of the line)
Blue line:
$x+y\ge-4$
$0+0\ge-4$
$0\ge-4$ (true, so we shade the right side of the line)
Red line:
$y\le2$
$0\le2$ (true, so we shade below the line)
The solution area is the overlap of all three shaded areas. The solution area is the triangle formed by the points $(-6,2)$, $(-3, -1)$, and $(3,2)$.
