Graph the solution set of the system.
-2x-y>=6
y>=-6
x>=-2
To graph the solution set of the system, we will first graph the inequalities on a coordinate plane.
For the first inequality -2x - y ≥ 6, we will first graph the line -2x - y = 6. To graph a line, we need to find two points on the line. We can choose x = 0 to find the y-intercept, and y = 0 to find the x-intercept.
When x = 0, we have -2(0) - y = 6, which simplifies to -y = 6, and then y = -6. So the y-intercept is (0, -6).
When y = 0, we have -2x - (0) = 6, which simplifies to -2x = 6, and then x = -3. So the x-intercept is (-3, 0).
Therefore, we can plot these two points and draw a line passing through them.
Next, let's graph the inequality y ≥ -6. Since this inequality is y = -6, it represents a horizontal line passing through y = -6.
Lastly, let's graph the inequality x ≥ -2. Since this inequality is x = -2, it represents a vertical line passing through x = -2.
Now, let's put everything together on a graph:
First, plot the two points (0, -6) and (-3, 0) for the line -2x - y = 6.
Next, draw a dashed line passing through these two points. The line should extend infinitely in both directions.
Then, draw a solid line representing the inequality y ≥ -6. This line should be a horizontal line passing through y = -6.
Finally, draw a solid line representing the inequality x ≥ -2. This line should be a vertical line passing through x = -2.
The shaded region where the lines and the inequalities overlap is the solution set of the system.
The graph should resemble a quadrilateral with the bottom right vertex at (-2, -6).