Answer
(-1, -3) or (1, 3) or (3, 1) or (-3, -1)
Work Step by Step
xy = 3 can be written as $y = \frac{3}{x}$. Plug this into $x^{2} +y^{2} = 10$
$x^{2} +(\frac{3}{x})^{2} = 10$
$x^{2} + \frac{9}{x^{2}} = 10$
Multiply both sides by $x^{2}$
$x^{4} + 9 = 10x^{2}$
$x^{4} - 10x^{2}+ 9 = 0$
Factor
$(x^{2} - 1)(x^{2} - 9) = 0$
$x^{2} - 1 = 0$ or $x^{2} - 9 = 0$
x = -1 or 1 or 3 or -3
Plug x values into $y = \frac{3}{x}$
$y = \frac{3}{-1}$ = -3
$y = \frac{3}{1}$ = 3
$y = \frac{3}{3}$ = 1
$y = \frac{3}{-3}$ = -1
(-1, -3) or (1, 3) or (3, 1) or (-3, -1)
