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Question
Solve the following system of inequalities graphically: x + y≥ 4, 2x – y > 0
Solution
x + y≥ 4 … (1)
2x – y > 0 … (2)
The graph of the lines, x + y = 4 and 2x – y = 0, are drawn in the figure below.
Inequality (1) represents the region above the line, x + y = 4 (including the line x + y = 4).
It is observed that (1, 0) satisfies the inequality, 2x – y > 0. [2(1) – 0 = 2 > 0]
Therefore, inequality (2) represents the half plane corresponding to the line, 2x – y = 0, containing the point (1, 0) [excluding the line 2x – y > 0].
Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on line x + y = 4 and excluding the points on line 2x – y = 0 as follows.
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