Question

The inequality 2x - 3y > 5 is satisfied by which of the following points?

(1,-1)
(1/2, 1/3)
(-1/2, 1/3)
(7/2, 1/3)

Answer 1

(7/2,1/3)
2x - 3y > 5
2 * 7/2 = 7
3 * 1/3 = 1
7-1 =6
6>5

Answer 2

Answer: (7/2, 1/3)

Explanation:

Given inequality: 2x - 3y > 5

Let's check all the options

1. (1,-1)

Put x=1 and y=-1 in the given inequality, we get

`2(1)-3(-1)=2+3=5\\gtr5`

2. (1/2, 1/3)

Put x=
`(1)/(2)` and y=
`(1)/(3)` in the given inequality, we get

`2((1)/(2))-3((1)/(3))=1-1=0\\gtr5`

3. (-1/2, 1/3)

Put x=
`(-1)/(2)` and y=
`(1)/(3)` in the given inequality, we get

`2((-1)/(2))-3((1)/(3))=-1-1=-2\\gtr5`

4. (7/2, 1/3)

Put x=
`(7)/(2)` and y=
`(1)/(3)` in the given inequality, we get

`2((7)/(2))-3((1)/(3))=7-1=6>5`

Thus, (7/2, 1/3) is the point which satisfy the given inequality.