The sum of 2 numbers equal 10 and the difference is 6
Answers
Question
The sum of 2 numbers equal 10 and the difference is 6 , then find the these values.
Solution
Given:-
- Sum of two number = 10
- Difference of two number = 6
Find:-
- These values.
Explanation
Let,
- first number be = x
- Second number be = y
A/c to question,
(Sum of two number = 10)
➥ x + y = 10 -----------(1)
Again,
( Difference of two number = 6 )
➥ x - y = 6 ---------------(2)
Sum of equation (1) and equation (2)
➥ 2x = 16
➥ x = 16/2
➥ x = 8
keep value of x in equation, (2)
➥ 8 - y = 6
➥ y = 8 - 6
➥ y = 2
Thus:-
- Value of x = 8. [Ans]
- Value of y = 2. [Ans]
____________________
Verification
Case(1):-
(Sum of two number = 10)
➥ x + y = 10
keep value of x and y ,
➥ 8 + 2 = 10
➥ 10 = 10
L.H.S = R.H.S
Case(2):-
( Difference of two number = 6 )
➥ x - y = 6
keep value of x and y
➥ 8 - 2 = 6
➥ 6 = 6
L.H.S. = R.H S
That's proved.
✮ The sum of two numbers = 10
✮ The difference between them = 6
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✮ The value of these two numbers...
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Let the one number be x...
Let the second number be y...
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In case 1...
---➣ x + y = 10 ________ eq 1...
⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀
In case 2...
---➣ x - y = 6 _________ eq 2...
⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀
From equation 1st and 2nd...
⠀⠀⠀⠀ ⠀ x + y = 10 ________ eq 1...
⠀⠀ ⠀ ⠀⠀x - y = 6 ________ eq 2...⠀⠀
⠀⠀ ⠀ ⠀-⠀ +⠀⠀-⠀⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀_______________⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⠀ 2y = 4
⠀⠀⠀⠀ ⠀ ⠀⠀y = ⠀
---➣
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Substituting the value of y in equation 1 to find the value of x...
---➣ x + y = 10 ________ eq 1...
---➣ x + 2 = 10
---➣
Therefore, the value of x is 8 and the value of y is 2...
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