SOLUTION: One number is 6 more than twice another. Their product is 6 more than twice their sum. Find the numbers x and y

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Question 468297: One number is 6 more than twice another. Their product is 6 more than twice their sum. Find the numbers x and y
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

One number is 6 more than twice another

Let x and ( 2x+6) represent the numbers

Question states***

 x(2x+6) = 2[x + (2x+6)] + 6

Solving for x

 2x^2 + 6x = 6x + 18

  2x^2 = 18

   x^2 = 9

    x = ± 3

Numbers are 3 and 12   OR -3 and 0

CHECKING our Answer***

   3*12 = 2*15 + 6 = 36

   -3*0 = 0 = 2*(-3) + 6