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in Linear Equations by (15.7k points)

Solve the given inequalities 2x – y ≤ –2, x – 2y ≥ 0, x ≥ 0, y ≥ 0graphically in two – dimensional plane.

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1 Answer

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by (15.2k points)

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,

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