x = one positive number

y = other positive number

x - y = 27 ← difference is 27

xy = 2680 ← product is 2680

x - y = 27 ← first equation

x = y + 27 ← added y to each side

xy = 2680 ← second equation

(y + 27)y = 2680 ← substituted (y + 27) for x

y² + 27y = 2680 ← distributive property

y² + 27y - 2680 = 0 ← subtracted 2680

(y + 67)(y - 40) = 0 ← factored

y + 67 = 0 or y - 40 = 0 ← set equal to zero

y = -67 or y = 40 ← solved

40 and 67 are the two numbers

- Proof

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