Question

The sum of 2 numbers equal 10 and the difference is 6

Answer 1

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.

Answer 2

$\underline{\underline\textbf{Given...}}$

✮ The sum of two numbers = 10

✮ The difference between them = 6

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

$\underline{\underline\textbf{To\:find...}}$

✮ The value of these two numbers...

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀⠀

$\underline{\underline\textbf{Solution...}}$

Let the one number be x...

Let the second number be y...

⠀⠀⠀⠀ ⠀ ⠀

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 = $\sf\dfrac{4}{2}$⠀

---➣ $\boxed{\sf{\red{\:y\:=\:2}}}$

⠀⠀⠀⠀ ⠀ ⠀⠀ ⠀⠀

Substituting the value of y in equation 1 to find the value of x...

---➣ x + y = 10 ________ eq 1...

---➣ x + 2 = 10

---➣ $\boxed{\sf{\red{\:x\:=\:8}}}$

Therefore, the value of x is 8 and the value of y is 2...

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