What is the graph of the system?
y ≤ −x − 1
y ≥ 2x + 4
Would I use elimination for this?
the solution is not just a point, which you could get by using elimination.
y <= x-1 is the whole half-plane, below the line y = x-1
y >= 2x+4 is the whole half-plane above the line y = 2x-4
So, graph those two lines and shade in the area which is below the first line and above the second line:
http://www.wolframalpha.com/input/?i=solve+y+%E2%89%A4+%E2%88%92x+%E2%88%92+1,+y+%E2%89%A5+2x+%2B+4
Include the lines (draw them as solid lines) because the inequalities both include "equal to." If they had been
y < −x − 1
y > 2x + 4
then you'd draw dashed lines to indicate that the boundaries are not to be included.
Thanks for the help
To determine the graph of the system of inequalities y ≤ -x - 1 and y ≥ 2x + 4, you can start by graphing the individual inequalities.
First, graph the inequality y ≤ -x - 1:
1. Start by graphing the line y = -x - 1 (without the inequality symbol).
2. Since the inequality symbol is "≤" (less than or equal to), you need to shade the region below the line to include the points on the line itself.
Next, graph the inequality y ≥ 2x + 4:
1. Graph the line y = 2x + 4 (without the inequality symbol).
2. Since the inequality symbol is "≥" (greater than or equal to), you need to shade the region above the line to include the points on the line itself.
Now, to find the graph of the system, you need to determine the overlapping region of the two individual graphs.
To do this, you can visually identify the region where the shaded regions of both graphs overlap. This represents the solution to the system of inequalities.
Regarding the second part of your question, elimination is a method used to solve systems of equations by eliminating one variable. In this case, since you have a system of inequalities, not equations, the elimination method doesn't apply. Graphing is the most suitable method to determine the solution to the system of inequalities in this scenario.