Answer
(2, 2) or (-2, -2)
Work Step by Step
xy = 4 can be written as y = $\frac{4}{x}$. Plug this into $x^{2} + y^{2} = 8$
$x^{2} + (\frac{4}{x})^{2} = 8$
$x^{2} + \frac{16}{x^{2}} = 8$
Multiply both sides by $x^{2}$
$x^{4} + 16 = 8x^{2}$
$x^{4} - 8x^{2} + 16 = 0$
$(x^{2} - 4)(x^{2} - 4) = 0$
x = 2 or -2
Plug x-values into y = $\frac{4}{x}$
y = $\frac{4}{2}$ = 2
y = $\frac{4}{-2}$ = -2
(2, 2) or (-2, -2)
