Answer
Please see the graph.
Work Step by Step
Red line: $2y-x\ge1$
Blue line: $x+y\ge4$
Green line: $y\le2$
Since all three lines are either "greater than or equal to" or "less than or equal to", solid lines are used.
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $2y-x\ge1$
$2y-x\ge1$
$2*0-0\ge1$
$0-0 \ge 1$
$0 \ge 1$
This is false, so we shade the side of the line that doesn't have the point.
Blue line: $x+y\ge4$
$x+y\ge4$
$0+0\ge4$
$0 \ge4$
This is false, so we shade the side of the line that doesn't have the point.
Green line: $y\le2$
$y\le2$
$0\le2$
This is true, so we shade the side of the line that has the point.
The solution of the set of equations is shaded by all three lines.
