Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10

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Solution

2x + y= 8 … (1)

x + 2y = 10 … (2)

The graph of the lines, 2x + y= 8 and x + 2y = 10, are drawn in the figure below.

Inequality (1) represents the region above the line, 2x + y = 8, and inequality (2) represents the region above the line, x + 2y = 10.

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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