Question

Which ordered pairs are solutions to the inequality 2x+y>−4?

Select each correct answer.



(5, −12)

(−3, 0)

(−1, −1)

(0, 1)

(4, −12)

Answer 1

we will proceed to resolve each case to determine the solution

we have

`2x+y>-4`

`y>-2x-4`

we know that

If an ordered pair is the solution of the inequality, then it must satisfy the inequality.

case a)
`(5,-12)`

Substitute the value of x and y in the inequality

`-12>-2*5-4`

`-12>-14` ------> is True

therefore

the ordered pair
`(5,-12)` is a solution of the inequality

case b)
`(-3,0)`

Substitute the value of x and y in the inequality

`0>-2*-3-4`

`0>2` ------> is False

therefore

the ordered pair
`(-3,0)` is not a solution of the inequality

case c)
`(-1,-1)`

Substitute the value of x and y in the inequality

`-1>-2*-1-4`

`-1>-2` ------> is True

therefore

the ordered pair
`(-1,-1)` is a solution of the inequality

case d)
`(0,1)`

Substitute the value of x and y in the inequality

`1>-2*0-4`

`1>-4` ------> is True

therefore

the ordered pair
`(0,1)` is a solution of the inequality

case e)
`(4,-12)`

Substitute the value of x and y in the inequality

`-12>-2*4-4`

`-12>-12` ------> is False

therefore

the ordered pair
`(4,-12)` is not a solution of the inequality

Verify

using a graphing tool

see the attached figure

the solution is the shaded area above the line

The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality