Answer
$(8,5)$ and $(-5,-8)$
Work Step by Step
Factor the left-hand side of the second equation
$x-y=3$
$(x-y)(x^2+xy+y^2)=387$
Substitute the first equation to the second one
$3(x^2+xy+y^2)=387$
$x^2+xy+y^2=129$
The system is equivalent to the following system:
$y=x-3$
$x^2+xy+y^2=129$
Substitute the first equation to the second one:
$x^2+x(x-3)+(x-3)^2=129$
$x^2+x^2-3x+x^2-6x+9-129=0$
$3x^2-9x-120=0$ Divide by 3
$x^2-3x-40=0$
$(x+5)(x-8)=0$
$x=-5$ and $x=8$
Obtain $y$:
For $x=8$, $y=8-3=5$
For $x=-5$, $y=-5-3=-8$
Therefore, the solutions are $(8,5)$ and $(-5,-8)$.
