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