Solve the following system of linear inequalities: 3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4

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

3x + 2y ≥ 24

Line: 3x + 2y = 24

Also, (0, 0) doesn’t satisfy the 3x + 2y ≥ 24, hence region is away from the origin

3x + y ≤ 15

Line: 3x + y = 15

Also, (0, 0) satisfies the 3x + y ≤ 15, hence region is towards the origin

x ≥ 4 implies that region is right to the line x = 4, therefore graph is

It is clear from the graph the above system has no common region as solution