Question

Which of the following points lie in the solution set to the following system of inequalities?

y > −3x + 3
y > x + 2

a
(2, −5)

b
(−2, 5)

c
(2, 5)

d
(−2, −5)

Answer 1

Option c . (2, 5)

Explanation:

we know that

If a ordered pair lie in the solution set of a system of inequalities, then the ordered pair must satisfy both inequalities of the system

we have

`y > -3x+3` ----> inequality A

`y >x+2` ----> inequality B

Verify each ordered pair

case a) (2,-5)

Verify inequality A

`y > -3x+3`

`-5 > -3(2)+3`

`-5 > -3` ----> is not true

so

The point not satisfy inequality A

therefore

The point not lie in the solution set

case b) (-2,5)

Verify inequality A

`y > -3x+3`

`5 > -3(-2)+3`

`5 > 9` ----> is not true

so

The point not satisfy inequality A

therefore

The point not lie in the solution set

case c) (2,5)

Verify inequality A

`y > -3x+3`

`5 > -3(2)+3`

`5 > -3` ----> is true

so

The point satisfy inequality A

Verify inequality B

`y >x+2`

`5 >2+2`

`5 >4` ---> is true

so

The point satisfy inequality B

therefore

The point lie in the solution set

case d) (-2,-5)

Verify inequality A

`y > -3x+3`

`-5 > -3(-2)+3`

`-5 > 9` ----> is not true

so

The point not satisfy inequality A

therefore

The point not lie in the solution set