Let x represent the larger number and y represent the smaller number ." The difference between two numbers is 13."

"Six times the larger number Is 19 times the smaller number."

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The first sentence can be written mathematically x-y=13 (1)

The second one can be written mathematically 6x=19y (2)

We have to solve this system

(1) can be transformed (multiplying by 6) 6x-6y=6*13=78

We replace 6x by 19y as written in (2) so 19y-6y=78 then 13y=78 and Finally y=6

from (1) x=13+y=19

x=19

y=6

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