Answer:
0
Explanation:
Multiplying the first equation by xy, we have ...
x^2 +y^2 = -xy
Factoring the expression of interest, we have ...
x^3 -y^3 = (x -y)(x^2 +xy +y^2)
Substituting for xy using the first expression we found, this is ...
x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0
The value of x^3 -y^3 is 0.