Question

What is the graph of the system?
y ≤ −x − 1
y ≥ 2x + 4

Would I use elimination for this?

Answer 1

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.

Answer 2

Thanks for the help