Answer
$(\pm2,1)$
Work Step by Step
Adding $-3$ times the first equation to the second one, we get:
$2y^3=2\\y^3=1\\y=1$
Plugging this back into the first equation, we get:
$x^4+1^3=17\\x^4=16\\x=\pm2$
Hence, the solutions are: $(\pm2,1)$