Question

Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≥ –1?

Answer 1

Part A
Part B
Part C
Part D

Answer 2

Part D

Answer 3

how do you know?

Answer 4

All we hve to do, is take an arbitrary point an evaluate to see if the inequalities are satisfied:
We take the first one and evaluate it with the origin (0,0):
\[y \ge x+1\]
\[0 \ge 0+1\]
\[0 \ge 1 (absurd)\]
so we conclude that parts C and D are the regions for the first inequality.
So we take the second:
\[y + x \ge -1\]
\[0 + 0 \ge -1\]
\[0 \ge -1\]
That is actually true, so we can conclude that the origin actually belongs in the region that satisfies the second inequality.
That would be: A and D

In order to find the region that satisfies both inequalities, we have to see what regions they have in common, so...
The solutions for the first were C and D,
and for the second were A and D.
The region "D" is the only one they have in common, so we conclude that the answer is part "D".

Answer 5

wow

Answer 6

thanks :)

Answer 7

i so understand now