Question 505059
Let 
One number = x
Another number = y
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Given
One number is five more than four times another
x+5=4y
x-4y=-5………………(1)
Their sum is 35
x+y=35……………..(2)

Minus (2) from (1)
x-4y=-5………………(1)
-x-y=-35……………..(2)
-5y=-40
y=-40/-5
 y=8
Put the value of y in (2)
x+y=35……………..(2)
x+8=35
x=35-8
x=27
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One number = x=27
Another number = y=8
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Check
Put the values of x and y in (1)
x-4y=-5………………(1)
27-4(8)=-5
27-32=-5
-5=-5
Put the values of x and y in (2)
x+y=35……………..(2)
8+27=35
35=35