Answer
Please see the graph.
Work Step by Step
Orange line: $3x+4y \leq12$
Red line: $x-2y > 6$
To determine what sides of the lines to shade, we pick the point $(0,0)$ and determine if the inequalities are valid. We will use a solid orange line and a dotted red line since the two inequalities respectively have a less than or equal to sign and a greater than sign.
$(0,0)$
$3x+4y \leq12$
$3*0+4*0 \leq12$
$0+0 \leq 12$
$ 0 \leq 12$ (true, so we shade the side of the line with the point)
$(0,0)$
$x-2y > 6$
$0-2*0 > 6$
$0 - 0 > 6$
$0 > 6$ (false, so we shade the side of the line with the point)
The overlap of the two graphs is the solution set for the system.
