Question

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.

Answer 1

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)

Answer 2

(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))

Answer 3

oops thats suppose to read (x,x/(x-1))

Answer 4

im so confused lol

Answer 5

what part?

Answer 6

(x,x/(x-1))

Answer 7

is dat the answer?

Answer 8

yes (x,x/(x-1)) , x does not equal 1

Answer 9

k

Answer 10

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

Answer 11

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)