Given x^2 + y^2 = 36 and xy = -10 find x + y.

This looks fun

ok so
we will use subsitution
xy=-10
divide both sides by x or y (I will choose y)
x=-10/y

sub -10/y fo x

(-10/y)^2+y^2=36
100/(y^2)+y^2=36
times both sides by y^2
100+y^4=36y^2
minus 36y^2 from both sides
y^4-36y^2+100=0
(y^2)^2-36(y^2)+100=0
quadratic formula
for
ax^2+bx+c=0
x=
x=
x=

sub
y=-10/x
y=

so x+y=+
multiply first number by and add them

x+y=
or
x+y= or

Aline graph should be used