If x-y=9, and x^2+y^2=99, what is xy? Show steps.

First rearrange the first equation: X - y = 9 => y = 9-x
Then substitute into the quadratic:
X^2 + y^2 =
x^2 + (9-x)^2 =
x^2 + (9-x)(9-x) =
x^2 + 81 -18x + x^2 =
2x^2 -18x + 81 = 99

Now solve for x, calculate y and then you can calculate their product.

(x-y)^2=81
x^2+ y^2 -2xy=81
2xy=x^2 + y^2 -81
xy=99-81 /2
xy =8/2
xy=4 is the answer...