[[1]] is a pair of integers whose difference is -5.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We are asked to find a pair of integers whose difference is -5
Suppose a pair of integers required as x, y ∈ Z such that
⇒x−y=−5..........equation(s)
We know that to solve linear equations of two variables we need equations.
Here we see that there is only one equation in two variables and we have no terms for the second equation.
Assume that the second equation as
⇒x=1...........equation(ii)
Now by substituting the required value from equation (ii) into equation (i) we get
⇒1−y=−5
⇒y=6
So we can conclude that the pair of integers whose difference is -5 is (1,6)
Here we assume that the second equation is x=1, but we can take any value of x
or y forms a pair of integers that gives a difference of -5.
So let's take the second equation in a different way, as follows.
So suppose the second equation as
⇒y=1..........equation(iii)
Now by substituting the required value from equation (iii) into equation (i) we get
⇒x−1=−5⇒x=−4
So we can conclude that the pair of integers whose difference is -5 is (-4,1)
Here we see that assuming the second equation of our choice, we get an infinite number of pairs.
We are asked to find a pair. So we can conclude that a pair like (1,6).

Watch 3-min video & get full concept clarity