Write a system of linear inequalities that describes the shaded region.

Question

Write a system of linear inequalities that describes the shaded region. ​  ​

Quizplus · Accepted Answer

The shaded region is bounded by the lines x = 0, y = 0, x + y = 5, and y = 1.

We can translate these into equations as follows: 
x ≥ 0 
y ≥ 0 
y ≤ 1 
x + y ≤ 5

Converting these into inequalities, we get: 
x ≥ 0 
y ≥ 0 
y ≤ 1 
-x - y ≤ -5

However, we need to flip the inequality for the last equation so that it matches the direction of the shading. Thus, our final system of linear inequalities is: 
x ≥ 0 
y ≥ 0 
y ≤ 1 
x + y ≥ 5

This matches the system of inequalities in choice (B).

Write a System of Linear Inequalities That Describes the Shaded