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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.

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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.

Answer options:
First Number
Second Number
Total
Added
Multiplied
20
First equation




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    1 Answer

    1. Quizzma Team

      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

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