The graphical representation of 3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4 is given by common region in the figure below.
3x + 2y ≥ 24 ....... (1)
3x + y ≤ 15 ...... (2)
x ≥ 4 .......... (3)
Inequality (1) represents the region above line 3x + 2y = 24 (including the line 3x + 2y = 24).
Inequality (2) represents the region below line 3x + y = 15(including the line 3x + y = 15).
Inequality (3) represents the region in front of line x = 4(including the line x = 4).
Therefore, we can see in the figure that there is no common shaded region.
So there linear inequalities in equations has no solution.
This can be represented as follows,
