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Solve the following system of inequalities graphically: 2*x* – *y* > 1, *x* – 2*y* < –1

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#### Solution

2*x* – *y* > 1 … (1)

*x* – 2*y* < –1 … (2)

The graph of the lines, 2*x* – *y* = 1 and *x* – 2*y *= –1, are drawn in the figure below.

Inequality (1) represents the region below the line, 2*x* – *y* = 1 (excluding the line 2*x* – *y* = 1), and inequality (2) represents the region above the line, *x* – 2*y *= –1 (excluding the line *x* – 2*y *= –1).

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

Concept: Solution of System of Linear Inequalities in Two Variables

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