Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10

$2 x+y=8 \ldots(1)$

$x+2 y=10 \ldots(2)$

The graph of the lines, $2 x+y=8$ and $x+2 y=10$, are drawn in the figure below.

Inequality (1) represents the region above the line, $2 x+y=8$, and inequality ( 2 ) represents the region above the line, $x+2 y=10$

Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines as follows.