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If 2+a is divisible by 11 and 35-b is divisible by 11 prove that a+b is divisible by 11 too

Respuesta :

Answer: see below

Step-by-step explanation  

Let    2 + a = 11 x

Let    35 - b = 11 y

Where x and y are any unknown integer

subtract the two equations

- 33 + a + b = 11 (x+y)

a+ b = 11 (x+ y) +33

a+ b = 11 (x+y) + 3 (11)

a+ b = 11(x+ y+3)

Which proves that a+b is a  factor of 11

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