Solve the following system of inequalities graphically: 2x + y≥ 4, x + y ≤ 3, 2x – 3y ≤ 6

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Solution

2x + y≥ 4 … (1)

x + y ≤ 3 … (2)

2x – 3y ≤ 6 … (3)

The graph of the lines, 2x + y= 4, x + y = 3, and 2x – 3y = 6, are drawn in the figure below.

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

x + y = 3 (including the line x + y = 3). Inequality (3) represents the region above the line, 2x – 3y = 6 (including the line 2x – 3y = 6).

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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