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asdf123

  • 5 years ago

If x and y are integers, list ALL of the ordered pairs (x,y) such that the product of x and y equals the sum of x and y.

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  1. myininaya
    • 5 years ago
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    xy=x+y means xy-y=x means y(x-1)=x means y=x/(x-1). So any ordered pair in this form (x,x/(x-1)) is an oder pair who has its product =to its sum. example: let x=2. Then we have (2,2). We know it holds for (2,2) since 2+2=2(2). How about for x=3. Then we have (3,3/2) We know it holds for (3,3/2) since 3+3/2=3(3/2)

  2. myininaya
    • 5 years ago
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    (x,y) product means x*y sum means x+y product=sum means xy=x+y Solve for either y or x. I chose y in the above. xy-y=x+y-y subtracted y on both sides y(x-1)=x now dividing x-1 on both sides gives y=x/(x-1) The order pair who has it sum=to its product is (x,x,/(x-1))

  3. myininaya
    • 5 years ago
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    oops thats suppose to read (x,x/(x-1))

  4. asdf123
    • 5 years ago
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    im so confused lol

  5. myininaya
    • 5 years ago
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    what part?

  6. asdf123
    • 5 years ago
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    (x,x/(x-1))

  7. asdf123
    • 5 years ago
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    is dat the answer?

  8. myininaya
    • 5 years ago
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    yes (x,x/(x-1)) , x does not equal 1

  9. asdf123
    • 5 years ago
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    k

  10. myininaya
    • 5 years ago
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    x+y=x/(x-1)={x(x-1)+x}/(x-1)=(x^2-x+x)/(x-1)=x^2/(x-1) xy=x(x/(x-1)=x^2/(x-1) so x+y=xy we just checked our work

  11. myininaya
    • 5 years ago
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    i missed my x in x+y its suppose to read x+y=x+x/(x-1)=[x(x-1)+x]/(x-1)=[x^2-x+x]/(x-1)=x^2/(x-1)

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