Question

6.Check whether the half plane x+2y ≥ 4 contains origin ​

Answer 1

Given : x+2y ≥ 4

To Find : whether the half plane x+2y ≥ 4 contains origin ​

Solution:

x+2y ≥ 4

origin ( 0 ,0)

if  x+2y ≥ 4 contains origin ​ then origin will satisfy the inequality

x = 0

y = 0

0 + 2(0)  ≥ 4

=> 0 ≥ 4

Hence not satisfied

=> the half plane x+2y ≥ 4 does not contain  origin ​

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Answer 2

Given : x+2y ≥ 4

To Find : whether the half plane x+2y ≥ 4 contains origin ​

Solution:

x+2y ≥ 4

origin ( 0 ,0)

if  x+2y ≥ 4 contains origin ​ then origin will satisfy the inequality

x = 0

y = 0

0 + 2(0)  ≥ 4

=> 0 ≥ 4

Hence not satisfied

=> the half plane x+2y ≥ 4 does not contain  origin ​