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

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Answer 1 · 2017-05-14T22:54:05

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:

$xy = -28$

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