Write a pair of negative integers whose difference gives 10 and whose sum is -10.

Expert Answers
hala718 eNotes educator| Certified Educator

Assume that the integers are n and m

We know that:

  n-m=10   ==> n=m+10

And n+m =-10 

Substitute with n=m+`10

m+10+m = -10

2m+10=-10

2m=-20

m=-10

n=0

 

neela | Student

Let n and m be the negative numbers. Let m < n. Then , the difference is:

n-m = 10 ...............(1) as given. And their sum is

n+m = -10..............(2)as given.

From (1) , n= m+10 and substitute this for n in eq(2):

(m+10)+m = -10.

2m+10 = -10.

2m = -10-10 = -20. So ,

m = -20. Or m = -20/2 =-10.

Therfore n = -n+10 = 0.

So the two numbers are -10 and 0. There are no other set of negative numbers satisfying the condition.