X^2-y^2=16 xy=15 Решите систему уравнений

$\left \{ {{ x^{2} - y^{2} =16} \atop {xy=15} } \right. \\ \left \{ {{ x^{2} - y^{2} =16} \atop {y= \frac{15}{x} } } \right. \\ x^{2} - (\frac{15}{x})^{2} =16 \\ x^{2} - \frac{225}{ x^{2} } =16 \\$

Замена:
$x^{2} = t \\ t - \frac{225}{t} = 16 \\ t^{2} - 16t - 225 = 0 \\ t=25, t = - 9 \\ \\ x^{2} =25 =\ \textgreater \ x=5, x=-5 \\ \\$
$y= \frac{15}{5} = 3, y= \frac{15}{-5} = -3 \\$

ОТвет: ( 5;3 ), ( -5;-3 ).