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 C best represents the solution set of the above two equations.

Explanation:

as we are given the graph of the following inequality

Now let us consider the first inequality -x+y≤1

on putting the point (0,0) in this inequality we get that 0≤1 which is true so the shaded region would be towards the origin. so it will cover Part C and Part D.

similarly on working for the second inequality x+y≤1 at (0,0) we get that 0≤-1 which is a false statement so the shading will go away from the region and it will cover Part B and Part C.

so the common region covered by both the inequalities is Part C.

Hence, the part which best represents the solution set of the following two inequalities is Part C.

Answer 2

1st equation : y ≤ x + 1

2nd equation: y + x ≤ –1
y ≤ -x -1

Part C is the answer.

1st equation represent Part C and Part D region.
2nd equation represent Part B and Part C region.

Part C is common among those.