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

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The graphical representation of  3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4 is given by common region in the figure below.

3x + 2y ≥ 24 ....... (1)

3x + y ≤ 15 ...... (2)

x ≥ 4 .......... (3)

Inequality (1) represents the region above line 3x + 2y = 24 (including the line 3x + 2y = 24). 

Inequality (2) represents the region below line 3x + y = 15(including the line 3x + y = 15). 

Inequality (3) represents the region in front of line x = 4(including the line x = 4). 

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,

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