Find all natural numbers a and b satisfying?

7 + a + b = 10

a + b = 3

b = 3 – a

assume values of a as 1, 2, 3,, ...

a = 1, b = 2

a = 2, b = 1

a = 3, b = 0 not natural number

solutions

a = 1, b = 2

a = 2, b = 1

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7+a+b = 10

a+b = 3

Only two values of a and b can satisfy the above equation.

If a = 1 then b = 2 and if

b = 2 then a = 1

a + b = 3

b = 3 - a

natural numbers will be greater or equal to 1

so b>= 1

3 - a>= 1

a <= 2

a >= 1(since it is a natural number)

so a takes 1 and 2.

for a = 1, b = 2 and for a = 2, b = 1

a=1 then b=2 or a=2 then b=1, only this two combination can be possible in natural no.

a + b =3

hence a = 1, 2, and b = 2,1

a=1 then b=2

b=1 then a=2;