Question

Which set of ordered pairs is a partial solution set for the system y<0 and x≤y?

(−1,−1),(−7,−6),(−8,−2),(−10,−3)
{(−6,−7),(−2,−8),(−3,−10),(0,−1)}
(−1,−1)∩(−7,−6)∩(−8,−2)∩(−10,−3)
{(−1,−1),(−7,−6),(−8,−2),(−10,−3)}

Answer 1

{(−1,−1),(−7,−6),(−8,−2),(−10,−3)}

Explanation:

we are given

y<0 and x≤y

so, we can write as

`x\leq y<0`

so, both values must be less than 0 or negative

we will verify each options

option-A:

Since,
`x\leq y<0`

So, all solution satisfies

so, this is TRUE

option-B:

Since,
`x\leq y<0`

x=-6 and y=-7

-7<-6

so, y<x

So, it does not satisfy solution

so, this is FALSE

option-C:

Since, solutions will be in points

intersection means interval

so, this is not valid solution

so, this is FALSE

option-D:

Since,
`x\leq y<0`

So, all solution satisfies

so, this is TRUE