11.2. Graph the solution set of the system of equations $\left\{\begin{array}{l}x-2 y=1 \\ x^{3}-6 x y-8 y^{3}=1\end{array}\right.$ on the coordinate plane.
Answer. The set of solutions is the line $y=\frac{x-1}{2}$. Solution. The second equation is a consequence of the first, since

$x^{3}-8 y^{3}-6 x y=(x-2 y)\left(x^{2}+2 x y+4 y^{2}\right)-6 x y=$ $=x^{2}+2 x y+4 y^{2}-6 x y=(x-2 y)^{2}=1$.