Question

___ +___= 8
+ +
___ - ___= 6
= =
13 8 ​

Answer 1

Answer:

3.5 + 4.5 = 8

+ +

9.5 - 3.5 = 6

-----------------

13 8

Answer 2

$\boxed{a}\:+\:\boxed{b}\:=\:8\\+\:\: \: \:\:\:\:\:\:+\\ \boxed{c}\:-\:\boxed{d}\:=\:6 \\=\: \:\:\:\:\:\:\:\:\:=\\ 13\:\:\:\:\:\:\: \:\:8$

We have to find the numbers whose sum (means sum of a and b) is 8.

So we have, a + b = 8, c - d = 6, a + c = 13 and b + d = 8

As per assumption;

⇒ a + b = 8

⇒ a = 8 - b...........(eq 1)

⇒ a + c = 13

Substitute value of a above

⇒ (8 - b) + c = 13

⇒ 8 - b + c = 13

⇒ - b + c = 5

⇒ c = 5 + b..........(eq 2)

Similarly, c - d = 6

Substitute value of c above

⇒ 5 + b - d = 6

⇒ b - d = 1

⇒ b = 1 + d...........(eq 3)

We have b + d = 8.

Now, put value of b i.e. of (eq 3) above

⇒ 1 + d + d = 8

⇒ 2d = 7

⇒ d = 7/2

⇒ d = 3.5

Now, substitute value of d in (eq 3)

⇒ b = 1 + 3.5

⇒ b = 4.5

Substitute value of b = 4.5 in (eq 2)

⇒ c = 5 + 4.5

⇒ c = 9.5

Substitute value of c = 9.5 in (a + c = 13)

⇒ a + 9.5 = 13

⇒ a = 13 - 9.5

⇒ a = 3.5

Therefore,

$\boxed{3.5}\:+\:\boxed{4.5}\:=\:8\\+\:\: \:\:\:\:\:\: \: \:\:\:\:\:\:+\\ \boxed{9.5}\:-\:\boxed{3.5}\:=\:6 \\=\: \:\:\:\: \:\:\:\:\:\:\:\:\:\:=\\ 13\:\:\:\:\:\:\: \:\:\:\: \:\:\:\:8$