Show that the solution set of the following system of linear inequalities is an unbounded region 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0

Let’s plot the region of each inequality and then find the common region of all

2x + y ≥ 8

Line: 2x + y = 8

Also, (0, 0) doesn’t satisy the 2x + y ≥ 8, hence region is away from the origin

x + 2y ≥ 10

Line: x + 2y = 10

Also, (0, 0) doesn’t satisy the x + 2y ≥ 10, hence region is away from the origin

x ≥ 0, and y ≥ 0 implies that region is in first quadrant, therefore graph is

Clearly shaded region is unbounded.