Calculate solution set.

Question

x^2+4y^2=68
xy=8

Answer 1

y = 8/x

x^2 + 4 (64/x^2) = 68

x^4 - 68 x^2 + 256 = 0

let z = x^2
z^2 -68 x + 256 = 0

(z-64)(z-4) = 0

z = 64 or 4
so
x = 2 or -2 or 8 or -8
if x = 2, y = 4
if x = -2, y = -4
if x = 8, y = 1
if x = -8, y = -1