Solve the following systems of inequalities, graphically 2x + y ≥ 8, x + 2y ≥ 10.

(ii) x + 2y ≥ 10 ...(ii)

Graph of inequality (i): Let us draw the graph of the line 2x + y = 8

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

At x = 0, y = 8, we get the point (0, 8) on y-axis.

Putting x = y = 0 in (i) we get 0 > 8 which is false.

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

Graph of inequality (ii): Let us draw the graph of the line x + 2y = 10

At y = 0, x = 10 we get the point (10, 0) on x - axis
At x = 0, y = 5 we get the point (0, 5) on y - axis

Putting x = y = 0 in (ii) we get 0 ≥ 10 which is false.

Hence, half plane region 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.