Question

If R={(x,y):x, yen, y is the remainder when x is divided by 7}. Then sum of all numbers in range of R​

Answer 1

Answer:

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Step-by-step explanation:

x+2y=8 , Given x,y are natural numbers , which implies x,y>0

If y=1 , we get x=6

If y=2 , we get x=4

If y=3 , we get x=2

For y≥4 , x wont be a natural number

So the range of R is {1,2,3}

Answer 2

Answer:

The sum of all numbers in range of R​ is 0+1+2+3+4+5+6 = 21

Step-by-step explanation:

Let x = 7, ,8,9,10,11,12,13,14,...

When x = 7,the value of  y = 0 is the reminder

When x = 8,y = 1 is the reminder

When x = 9 y = 2 is the reminder

x = 10, y = 3 is the reminder

x=11,y=4 is the reminder

x=12, y=5 is the reminder

x = 13,y=6 is the reminder

x=14,y=0 is the reminder

It continues... so range is 0,1,2,3,4,5,6 .

So sum of all numbers in range of R​ is 0+1+2+3+4+5+6 = 21.