Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12

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Solution

2x + y≥ 6 … (1)

3x + 4y ≤ 12 … (2)

The graph of the lines, 2x + y= 6 and 3x + 4y = 12, are drawn in the figure below.

Inequality (1) represents the region above the line, 2x + y= 6 (including the line 2x + y= 6), and inequality (2) represents the region below the line, 3x + 4y =12 (including the line 3x + 4y =12).

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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