Question

10. The graph of the inequality 2x + 3y > 6 is

(a) half plane that contains the origin

(b) half plane that neither contains origin nor the points of the line 2x + 3y = 6.

(C) whole XOY-plane excluding the points on the line 2x + 3y = 6

(d) entire XOY-plane.

please answer fast it's urgent ​

Answer 1

The graph of the inequality 2x+3y>6 is

half plane that contains the origin.

half plane that neither contains the origin nor the points of the line 2x+3y=6

whole XOY - plane excluding the points on the line 2x+3y=6.

entire XOY plane.

Solution

half plane that neither contains the origin nor the points of the line 2x+3y=6

Given inequality 2x+3y>6

3y>6−2x

y>36−2x

Now consider y=36−2x and plot the graph [Ref. image 1]

 X 0 3 Y 2 0we used dashed as 

y>36−2x as there in no equal to sign

∵ y is greater than 36−2x we will shade the upper part  [Ref. image 2]

Thus the graph of 2x+3y>6 is drawn

HOPE IT HELPS YOU