Question

Solve the following system of inequalities graphically
$x+2y\le 8$ ......(1)
$2x+y\le 8$ ......(2)
$x\ge 0$ ......(3)
$y\ge 0$ ......(4)

Answer 1

We draw the graphs of the lines x + 2y = 8 and 2x + y = 8 The inequality (1) and (2) represent the region below the two lines including the point on the respective lines
Since $x\ge 0,y\ge 0$ every point in the shaded region in the first quadrant represent a solution of the given system of inequalities