Solve the following system of inequalities graphically: x + y ≤ 6, x + y ≥ 4

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Solution

x + y ≤ 6 … (1)

x + y ≥ 4 … (2)

The graph of the lines, x + y = 6 and x + y = 4, are drawn in the figure below.

Inequality (1) represents the region below the line, x + y = 6 (including the line x + y = 6), and inequality (2) represents the region above the line, x + y = 4 (including the line x + y = 4).

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

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