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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.

Concept: Solution of System of Linear Inequalities in Two Variables

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