Solve the following system of linear inequality graphically
$2 x + y \geq 6$ ......(1)
$x - y \leq 2$ ......(2)

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Solution

The graph of linear equation $2 x + y = 6$ is drawn in fig We note that solution of inequality (1) is represented by the shaded region above the line $2 x + y = 6$ including the point on the line
On the same set of axes we draw graph of the equation $x - y = 2$ as shown in the fig Then we not that inequality (2) represents the shaded region above the line $x - y = 2$ including the points on the line
Clearly the double shaded region common to the above two shaded region is the required solution region of the given system if inequalities

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