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Question
Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0
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Solution
x + y ≤ 9 ... (1)
y > x ... (2)
x ≥ 0 ... (3)
The graph of the lines, x + y= 9 and y = x, are drawn in the figure below.
Inequality (1) represents the region below the line, x + y = 9 (including the line x + y = 9).
It is observed that (0, 1) satisfies the inequality, y > x. [1 > 0]
Therefore, inequality (2) represents the half plane corresponding to the line, y = x, containing the point (0, 1) [excluding the line y = x].
Inequality (3) represents the region on the right hand side of the line, x = 0 or y-axis (including y-axis).
Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the lines, x + y = 9 and x = 0, and excluding the points on line y = x as follows.
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