let 'x' and 'y' represent the numbers

a first number plus twice a second number is 3

x + 2y = 3

twice the first number plus the second totals 9

2x + y = 9

by solving the system of equations:

x + 2y = 3

2x + y = 9

we find:

x = 5

y = -1

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indeed:

5 + 2*(-1) = 3

2*5 + (-1) = 9

the numbers are 5 and -1.