$\displaystyle \text{if } a\neq b\neq c\text{ and the equations}$

$\displaystyle ax+a^2y+(a^3+1)=0$

$\displaystyle bx+b^2y+(b^3+1)=0 $

$\displaystyle cx+c^2y+(c^3+1)=0$

$\displaystyle \text{are consistent, then prove that }abc=-1.$

I could use some desperately needed help on this one. My first plan of attack was to move all the terms with no variables onto one side. This gives us a system of equations with 3 equations but with only two unknowns,(I think the key is in this detail?) Does this mean that if I take any two equations, the one with a's and b's for example, and find the x and y solution that those two solutions will have to equal another x y solution I obtained from maybe using the equations with just b's and c's?

I have a feeling I'm totally off base. No one in my class has gotten this problem so anything would be helpful thanks.