Question

Look at the graph below: First line joins ordered pairs negative 4, 3 and 2, negative 3. Second line joins negative 4, negative 3 and 2, 3. Part A shaded above first and second line. Part B shaded below first line and above second line. Part C shaded below first and second lines. Part D shaded above first line and below second line. Which part of the graph best represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ −1? (5 points) Question 10 options: 1) Part A 2) Part B 3) Part C 4) Part D

Answer 1

It's Part B

Step-by-step explanation:

Got it right!

Answer 2

Final answer:

Part B of the graph is the correct representation of the solution set for the system of inequalities y ≥ x + 1 and y + x ≤ −1 because it shows the overlapping region shaded below the first line and above the second line.

Step-by-step explanation:

The question asks which part of the graph represents the solution set to the system of inequalities y ≥ x + 1 and y + x ≤ −1. To find the solution set for the system of inequalities, we need to graph both inequalities and see where their shaded regions overlap.

The inequality y ≥ x + 1 is graphed by drawing the line y = x + 1 (which has a positive slope) and shading the area above it, since the inequality includes greater than or equal to.

The inequality y + x ≤ −1 simplifies to y ≤ −x − 1 when we subtract x from both sides, and it is graphed by drawing the line y = −x − 1 (which has a negative slope) and shading the area below it, since the inequality is less than or equal to.

The solution set is the area where these two shaded regions overlap. Hence, Part B of the graph, which is shaded below the first line and above the second line, correctly represents the overlap of both inequalities and therefore the solution set to the system.