Two numbers have a sum of 9 when added together. The same two numbers have a product of 20 when multiplied together. Complete the table and write a system of equations to represent the two numbers.

To solve the problem, let’s define the two numbers as ( x ) and ( y ). Based on the information given, we can create the following system of equations:

1. ( x + y = 9 ) (their sum)
2. ( x cdot y = 20 ) (their product)

Now, let’s fill in the table:

– First Number: ( x )

– Second Number: ( y )

– Total: ( 9 )

– Added: ( 9 )

– Multiplied: ( 20 )

To find the specific values of ( x ) and ( y ), we can solve this system. From the first equation, we can express ( y ) in terms of ( x ):

[ y = 9 – x ]

Now, substitute ( y ) in the second equation:

[ x(9 – x) = 20 ]

Expanding this gives:

[ 9x – x^2 = 20 ]

Rearranging it:

[ x^2 – 9x + 20 = 0 ]

Now, we can factor the quadratic:

[ (x – 5)(x – 4) = 0 ]

This gives us the solutions:

[ x = 5 quad text{or} quad x = 4 ]

Thus, the two numbers are ( 5 ) and ( 4