Find the linear inequalities for which the shaded area is the solution set in the figure given below. 6x + 27 = 8, x + y = 4, x + 5y = 4

Question

Find the linear inequalities for which the shaded area is the solution set in the figure given below.

Answer 1

We have seen that the shaded region and origin are on the opposite side of the line 6x + 2y = 8 

For (0,0) we have 0 + 0 - 8 < 0 . So the shaded region satisfies the inequality 6x + 2y \(\ge\) 8. 

We have seen that the shaded region and origin are on the opposite side of the line x + 5y = 4 

For (0,0) we have 0 + 0 - 4 < 0 . So the shaded region satisfies the inequality x + 5y \(\ge\) 4 . 

We have seen that the shaded region and origin are on the same side of the line x + y = 4 

For (0,0) we have 0 + 0 - 4 < 0 . So the shaded region satisfies the inequality x + y \(\le\) 4 

We have seen that the shaded region and origin are on the same side of the line y = 3 

For (0,0) we have 0 - 3 < 0. So the shaded region satisfies the inequality y \(\le\) 3. 

Thus the linear inequation comprising the given solution set are +2y \(\ge\) 8,x + 5y \(\ge\) 4, x + y \(\le\)4, y \(\le\) 3