Let 'x' and 'y' represent the two integer numbers.

The sum of the numbers is 9 so we have:

x + y = 9

y = 9 - x

The product is 20 means:

x*y = 20

Plug y = 9 - x into xy = 20:

x(9 - x) = 20

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click here to see the equation solved for x

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x1 = 4

x2 = 5

For x = 4 we find y = 9 - 4 = 5.

For x = 5 we find y = 9 - 5 = 4.

The two numbers are 4 and 5.