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Let x be the smaller number and be the larger number. Then, x + y = 19 2x + 3y = 48

First equation can be transformed as x = 19 - y.

Substituting this value to the second equation, we have 2(19 - y) + 3y = 48 38 - 2y + 3y = 48 38 + y = 48 y = 48 - 38 y = 10

Substituting the value of y to either of the two equations, we have x + y = 19 x + 10 = 19 x = 19 - 10 x = 9