Answer
The solution set is the region shaded GRAY
.
Work Step by Step
We will graph the solution region for each inequality.
1.
$ 3x+y=6,\quad$ solid line $(\leq)$
x:intercept: $ 3x+0=6\quad$point: $(2,0)$
y:intercept: $ 0+y=6\quad$point: $(0,6)$
Test (0,0):$\quad 3(0)+0\leq 6?\quad$ Yes
Shade the region containing (0,0)
2.
$ x=-2,\quad$ dashed $( > )$,
vertical line passing through $(-2,0)$
Test (0,0):$\quad 0 > - 2?\quad$ Yes
Shade the region containing (0,0)
3.
$ y=4, \quad$ solid line $(\leq),$
horizontal line passing through $(0, 4)$
Test (0,0):$\quad 0\leq 4?\quad$ Yes
Shade the region containing (0,0)
If there is a solution set,
it is the region with ALL 3 shadings.
The solution set is the region shaded GRAY