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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.
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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myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0xy=x+y means xyy=x means y(x1)=x means y=x/(x1). So any ordered pair in this form (x,x/(x1)) 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)

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0(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. xyy=x+yy subtracted y on both sides y(x1)=x now dividing x1 on both sides gives y=x/(x1) The order pair who has it sum=to its product is (x,x,/(x1))

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oops thats suppose to read (x,x/(x1))

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0yes (x,x/(x1)) , x does not equal 1

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0x+y=x/(x1)={x(x1)+x}/(x1)=(x^2x+x)/(x1)=x^2/(x1) xy=x(x/(x1)=x^2/(x1) so x+y=xy we just checked our work

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i missed my x in x+y its suppose to read x+y=x+x/(x1)=[x(x1)+x]/(x1)=[x^2x+x]/(x1)=x^2/(x1)
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