Question

find positive integer solutions to 7x+6y=90​

Answer 1

Given : 7x + 6y = 90​

To Find : positive integer solutions

Solution:

7x + 6y = 90

0 < 7x < 90  => 0 < x ≤ 14

0 < 6y < 90  => 0 < y < 15

=> x + 6x + 6y = 90

=> x + 6(x + y) = 6 * 15

=>  x = 6(15 - x - y)

Hence  x must be a multiple of 6

0 < x ≤ 14  => x = 6 or 12 are possible values

x = 6

=> 6 = 6(15 - 6 - y)

=> 1 = 9 - y

=> y = 8

x = 12

=> 12 = 6(15 - 12 - y)

=> 2 = 3 - y

=> y = 1

positive integer solutions are

( 6 , 8)  & ( 12 , 1)

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