Answer
The solution set is the region shaded GRAY.
.
Work Step by Step
We will graph two lines and shade the solution region for each inequality.
1 (red)
$x+2y=4 \quad $solid line ( sign is $\leq )$,
x-intercept:$\quad x+0=4\quad$ point: ($4,0)$
y-intercept:$ \quad 0+2y=4\quad$ point: ($0,2)$
Testing (0,0):$\quad 0+2(0) \leq 4 \quad ?$
Yes, shade the region containing (0,0)
2 (blue)
$y=x-3 \quad $solid line ( sign is $\geq )$,
y-intercept: $y=-3$, point: ($0,-3)$
second point:$ x=3, $
$y=3-3=0$, point: $(3,0)$
Testing (0,0):$\quad 0\geq 0-3 \quad ?$
Yes, shade the region containing (0,0)
The solution set is the region with BOTH shadings
The solution set is the region shaded GRAY