Solve the following system of inequalities graphically:

2x + y ≥ 8, x + 2y ≥ 10

Given 2x + y 8

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y = 8 and x = 4

The required points are (0, 8) and (4, 0)

Checking if the origin is included in the line`s graph (0, 0)

0 ≥ 8, which is false

Hence the origin is not included in the solution area and the requires area would be the area to the right of line`s graph.

x + 2y 10

Putting value of x = 0 and y = 0 in equation one by one, we get value of

y = 5 and x = 10

The required points are (0, 5) and (10 , 0)

Checking for the origin (0, 0)

0 ≥ 10 which is false,

Hence the origin would not lie in the required solution area. The required area would be to the left of the line graph.

The shaded area in the graph is the required solution of the given inequalities.