xy=-2
x+y=6
minnus x from second equation
y=6-x
sub for y
x(6-x)=-2
6x-x^2=-2
add x^2 both sides and minus 6x both sides
0=x^2-6x-2
use quadatic formula
if you have
ax^2+bx+c=0
x=\(\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}\)
x^2-6x-2=0
a=1
b=-6
c=-2
x=\(\frac{-(-6)+/- \sqrt{(-6)^{2}-4(1)(-2)} }{2(1)}\)
x=\(\frac{6+/- \sqrt{36+8} }{2}\)
x=\(\frac{6+/- \sqrt{44} }{2}\)
x=\(\frac{6+/- 2\sqrt{11} }{2}\)
x=\(3+/- \sqrt{11}\)
x=\(3+ \sqrt{11}\) or x=\(3- \sqrt{11}\)
aprox
x=6.31662 or -0.316625
those are the numbers
6.31662 and -0.316625
