Question

Find the linear inequations for which the shaded area in figure is the solution set..Draw the diagram of the solution set of the linear inequations:

Answer 1

Consider the line 2x+3y=6

We observe that the shaded region and the origin are on the opposite sides of the line 2x+3y=6 and (0,0) does not satisfy the inequation $2x+3y\ge 6$

So,we must have one inequations as $2x+3y\ge 6$.

Consider the line 4x+6y=24

We observe that the shaded region and the origin are on the opposite sides of the line 4x+6y=24 and (0,0) does not satisfy the inequation $4x+6y\le 24$

So,the second inequations is $4x+6y\le 24$

Consider the line -3x+2y=3

We observe that the shaded region and the origin are on the opposite sides of the line -3x+2y=3 and (0,0) does not satisfy the inequation $-3x+2y\le 3$

So,the third inequations is $-3x+2y\le 3$

Finaly,consider the line x-2y=2

We observe that the shaded region and the origin are on the opposite sides of the line x-2y=2 and (0,0) does not satisfy the inequation $x-2y\le 2$

So,the forth inequations is $x-2y\le 2$

We also notice that the shaded region is above x-axis and is on the right side of y-axis.

So,we must have $x\ge 0andy\ge 0$

Thus,the linear inequations corresponding to the given solution set are $2x+3y\ge 6,4x+6y\le 24,-3x+2y\le 3,x-2y\le 2,x\ge 0,y\ge 0$