let 'x' and 'y' be the two integers such that x>y

the sum of two integers is 51

x + y = 51

the larger integer is 3 more than twice the smaller integer

x = 3 + 2y

by solving the system of equations

x + y = 51

x = 3 + 2y

we find

x = 35

y = 16

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the numbers are 35 and 16.