Answer
Please see the graph.
Work Step by Step
Green line: $3x-4y\ge-6$
Blue line: $2x+y\le7$
Orange line: $y\ge-3$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Green line: $3x-4y\ge-6$
$3x-4y\ge-6$
$3*0-4*0\ge -6$
$0-0\ge -6$
$0 \ge -6$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "greater than or equal to" sign, so we use a solid line.
Blue line: $2x+y\le7$
$2x+y\le7$
$2*0+0\le7$
$0+0 \le 7$
$0 \le 7$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "less than or equal to" sign, so we use a solid line.
Orange line: $y\ge-3$
$y\ge-3$
$0 \ge -3$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "greater than or equal" sign, so we use a solid line.
The solution area for the system on inequalities is the area that is shaded blue, green, and orange.
