Question

How do you determine the value of `xy` if `x+y=-3` and `x^2+y^2=65`?

Answer 1

First make the `x+y=-3` have common terms with the `x^2+ y^2= 65`.

You do this by squaring the entire `x+y=-3`, this will also get you the term `xy` that you want to find:

`(x+y)^2 = (-3)^2`

`x^2 + y^2 = 65`

Now make them equal to each other to:

`x^2 + 2xy + y^2 -9 = x^2 + y^2 -65`

Isolate the `2xy` by subtracting the `x^2 and y^2` from both sides also add a 9 to both sides to eliminate the 9 from the left side

You should get this:

`2xy = -56`

Then isolate the `xy` by dividing by 2 on both sides to get:

`xy = -28`