the area shaded with vertical lines is the solution set of the inequalities;
Attached Figure / Diagram
A
y ≤ x, y + 2x ≤ -3
B
y ≥ x, y + 2x ≥ - 3
C
y ≤ x, y ≤ 2x - 3, x ≤ 3
D
y ≤ -x, y ≤ 2x - 3, x ≤ 3
E
y ≥ x, y + 2x ≥ 3, x ≤ 3
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Vertical Line x = 3:
This line indicates a constraint on x, specifically that
x \le 3.(behind is shaded)
The line y + 2x = -3 or y = - 2x - 3
This line has a negative slope of -2 and intersects the y-axis at -3. The region below this line corresponds to
y \le − 2x − 3.
Line y = x:
.This line has a slope of 1 and passes through the origin. The region below this line corresponds to y \le x
The lines are all thick = strict inequalities.
Source: Myschool Past Questions Archive (Record #22649)