The graphical representation of 2x + y ≥ 6, 3x + 4y ≤ 12 is given by common region in the figure below.
2x + y ≥ 6 ..... (1)
3x + 4y ≤ 12 ..... (2)
Inequality (1) represents the region above line 2x + y = 6 (including the line 2x + y = 6 ).
Inequality (2) represents the region below line 3x+4y=12 (including the line 3x+4y=12).
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,