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