Question 1096469
<br>An unusual problem; I don't recall seeing anything quite like it before....<br>
Add the two equations and do some algebra:
{{{x^3+y^3 = 27x + 27y}}}
{{{(x+y)(x^2-xy+y^2) = 27(x+y)}}}
{{{x^2-xy+y^2 = 27}}}  <-- equation (1)<br>
Then subtract the two equations and do some similar algebra:
{{{x^3-y^3 = 13x - 13y}}}
{{{(x-y)(x^2+xy+y^2) = 13(x-y)}}}
{{{x^2+xy+y^2 = 13}}}  <-- equation (2)<br>
Now subtract equation (1) from equation (2):
{{{2xy = -14}}}
{{{xy = -7}}}<br>
Answer: xy = -7