The sum of two integers is thirty. eight times the smaller integer is 6 more than 5 times the larger interger. find the integers

First of all you must form equations. Now, 
Let the smaller integer = x and 
Let the greater integer = y 
x + y = 30 (1) Given. The sum of the integers 
8x = 5y + 6 or } Given. 8 times the smaller integer is 
8x - 5y = 6 (2)} bigger by 6 than 5 times the greater 
} integer.
(1) * 5, we get,
5x + 5y = 150 (3)

By adding Eq.(2) and (3), 
13x = 156
So x = 156/13 = 12
By replacing this value of x in Eq.(1), we get
12 + y = 30
So y = 30 - 12 = 18 
So, 12 and 18 are the integers.

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