Solve the following system of inequalities graphically: 2x – y > 1, x – 2y < –1

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Solution

2x – y > 1 … (1)

x – 2y < –1 … (2)

The graph of the lines, 2x – y = 1 and x – 2y = –1, are drawn in the figure below.

Inequality (1) represents the region below the line, 2x – y = 1 (excluding the line 2x – y = 1), and inequality (2) represents the region above the line, x – 2y = –1 (excluding the line x – 2y = –1).

Hence, the solution of the given system of linear inequalities is represented by the common shaded region excluding the points on the respective lines as follows.

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