Solve the following systems of inequalities graphically  x + y ≤ 6, x + y ≥ 4

x + y ≥ 4 ...(ii)

Graph of inequality (i): Let us draw the graph of the line x + y = 6.

At x = 0, x = 6, we get the point (6, 0) on x-axis.

At x = 0, y = 6, we get the point (0, 6) on y-axis.

Putting x = y = 0 in (0 we get 0 ≤ 6 which is true.

Hence, half-plane containing the origin is the solution region of the given inequality.

Graph of inequality (ii)': Let us draw the graph of the line x + y = 4.

At y = 0, x = 4 we get the point (4, 0) on x-axis.

At x = 0, y - 4 we get the point (0, 4) on y-axis.

Putting x - y - 0 in (ii) we get 0 > 4 which is false.

Hence half plane not containing the origin is the solution region of the given inequality.

The common region of the above two regions represent the solution set of the given linear constraints.