The graphical representation of 2x – y ≤ –2, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is given by common region in the figure below.
2x – y ≤ –2 ............ (1)
x – 2y ≥ 0 .......... (2)
x ≥ 0 ........... (3)
y ≥ 0 .......... (4)
Inequality (1) represents the region above line 2x – y = –2 (including the line 2x – y = –2).
Inequality (2) represents the region below line x – 2y = 0 (including the line x – 2y = 0).
Inequality (3) represents the region in front of line x = 0 (including the line x = 0).
Inequality (4) represents the region above line y = 0 (including the line y = 0).
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,