The graphical representation of 2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6 is given by common region in the figure below.
2x + y ≥ 4 ....... (1)
x + y ≤ 3 ....... (2)
2x – 3y ≤ 6 ....... (3)
Inequality (1) represents the region above line 2x + y = 4 (including the line 2x + y = 4).
Inequality (2) represents the region below line x + y ≤ 3 (including the line x + y ≤ 3 ).
Inequality (3) represents the region above line x + y ≤ 3 (including the line x + y ≤ 3).
Therefore, every point in the common shaded region including the points on the respective lines represents the solution for the given inequalities.
This can be represented as follows,