Solve the given inequalities 3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4, graphically in two – dimensional plane.

The graphical representation of


is given by common region in the figure below.


.…… (1)


……. (2)


……. (3)


Inequality (1) represents the region above line (including the line ).


Inequality (2) represents the region below line (including the line ).


Inequality (3) represents the region in front of line (including the line ).


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,



1