Answer
The system has no solutions.
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=3 \quad $dashed line ( sign is $> )$,
x-intercept:$\quad x+0=3\quad$ point: ($3,0)$
y-intercept:$ \quad 0+y=3\quad$ point: ($0,3)$
Testing (0,0):$\quad (0)+(0) > 3 \quad ?$
No, shade the region not containing (0,0)
2 (blue)
$x+y=-2 \quad $dashed line ( sign is $< )$,
x-intercept:$\quad x+0=-2\quad$ point: ($-2,0)$
y-intercept:$ \quad 0+y=-2\quad$ point: ($0,-2)$
Testing (0,0):$\quad 0+0 < -2 \quad ?$
No, shade the region not containing (0,0)
The solution set should be the region with BOTH shadings.
There is no region with both shadings here.
The solution set is empty, $\emptyset.$
The system has no solutions.
