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Question
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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