Solve the following system

x + 2y < 8 ….(i) 2x + y < 8

x ≥ 0 …(3)  y ≥ 0

We draw the graph of lines x + 2y = 8 and 2x + y = 8.

Let us take an inequality x + 2y < 8.

We take any point, say (0, 0), then equality becomes 0 + 2×0 < 8 ⇒ 0 < 8, which is true.

Hence, we shade the region where point (0, 0) lies.

For another inequality 2x + y < 8,

We take point (1, 1), then inequality becomes 2 + 1 < 8 ⇒ 3 < 8, which is true.

Hence, we shade the region where point (1, 1) lies.

Since x ≥ 0, y ≥ 0, every point in the shaded region lies in the first quadrant, which represents the solution of the given system of inequalities.

Hence, the doubly shaded region is the common solution of the given inequalities.