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Solve the given inequalities 2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6graphically in two – dimensional plane.

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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,

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