Question

A pair of integers whose sum is -10 and difference is 4

Answer 1

Answer:

–3 , –7

Solution:

Let the required integers be x and y .

Now,

According to the question , the sum of both the integers is –10 .

Thus,

x + y = -10 ------(1)

Also,

The difference between the integers is 4 .

Thus,

=> | x - y | = 4

=> x - y = ± 4

=> x - y = 4 -------(2.1) , x - y = -4 -------(2.2)

Here ,

Two cases arises.

Case(1) :

x + y = -10 -------(1)

x - y = 4 -------(2.1)

Adding eq-(1) and (2.1) , we get ;

=> x + y + x - y = -10 + 4

=> 2x = -6

=> x = -6/2

=> x = -3

Now,

Putting x = -3 in eq-(1) , we get ;

=> x + y = -10

=> -3 + y = -10

=> y = - 10 + 3

=> y = -7

Hence,

Required pair of integers are :

–3 , –7

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

Case(2) :

x + y = -10 -------(1)

x - y = -4 -------(2.2)

Adding eq-(1) and (2.2) , we get ;

=> x + y + x - y = -10 - 4

=> 2x = -14

=> x = -14/2

=> x = -7

Now,

Putting x = -7 in eq-(1) , we get ;

=> x + y = -10

=> -7 + y = -10

=> y = - 10 + 7

=> y = -3

Hence,

Required pair of integers are :

Required pair of integers are : –7 , –3

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

In both the cases , we got the same pair of integers , ie ; –3 , –7 .

Hence,

The required answer is ;

–3 , –7