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....
unless we know it is vertical or horizontal
1. (red)
$x+y=4 \quad $dashed line ( sign is $> )$,
x-intercept:$\quad x+0=4\quad$ point: ($4,0)$
y-intercept:$ \quad 0+y=4\quad$ point: ($0,4)$
Testing (0,0):$\quad (0)+(0) > 3 \quad ?$
No, shade the region not containing (0,0)
2 (blue)
$x+y=-1 \quad $dashed line ( sign is $> )$,
x-intercept:$\quad x+0=-1\quad$ point: ($-1,0)$
y-intercept:$ \quad 0+y=-1\quad$ point: ($0,-1)$
Testing (0,0):$\quad 0+0 > -1 \quad ?$
Yes, shade the region containing (0,0)
The solution set is the region with BOTH shadings.
The solution set is the region shaded GRAY