Question

Write down a pair of integers whose:
(i) Sum is 7
(ii) Difference is -10
(iii) Sum is 0

Answer 1

Hint: a) Given that the sum of two integers is 7. Let us consider that one of two integers whose sum is 7 be x then the other integer shall be \[7 - x\]. Now give any fixed integral value to x we get \[7 - x\] as well.
b) In question it is given that the difference of two integers is -10. Let us consider two integers whose difference is -10 be x, y. Give any fixed integral value to x we will get y as well.
c) In question it is asked to find the pair of integers whose sum is 0. Let us consider that one of two integers whose sum is 0 be x then by giving any fixed integral value to x we can get the other number as well.

Complete step-by-step solution:
a) Let x be one number and the other number be 7-x and by summing up both we get 7.
Let x=3 then
$7 - x = 7 - 3 \\
= 4 $
So, an integral pair whose sum is 7 is (3,4)

(b) Let the 2 integers whose difference is -10 be x, y. Then
$ x - y = - 10 \\
\Rightarrow x = - 10 + y \\
\Rightarrow x = y - 10 $
If y=3 then x =-7. So, an integral pair whose difference is -10 is (-7,3).

(c) Let x be one of the integers then the other integer is –x whose sum is 0.
If x=3 then –x=-3. So, an integral pair whose sum is 0 is (x,-x) = (3,-3).

Note: Here in this question, we have mentioned only one pair for each condition. Actually, there are an infinite number of integral pairs satisfying their individual conditions. The problem like this can be solved by fixing one variable then getting the equation of unknown variable in terms of fixed variable and then giving value to fixed variable eventually attains value of unknown variable.