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)
$2x-y=4 \quad $solid line ( sign is $\leq)$,
x-intercept: 2$x+0=4\Rightarrow x=2$
y-intercept: $0-y=4 \Rightarrow y=-4$
Testing (0,0):$\quad 2(0)-(0)\leq 4\quad ?$
Yes, shade the region containing (0,0)
2 (blue)
$3x+2y=-6 \quad $dashed line ( sign is $> )$,
x-intercept: $3x+0=-6\Rightarrow x=-2$
y-intercept: $0+2y=-6\Rightarrow y=-3$
Testing (0,0):$\quad 3(0)+2(0)>-6\quad ?$
Yes, shade the region containing (0,0)
The solution set is the region with BOTH shadings
The solution set is the region shaded GRAY