Let $k>1$ be an integer and let $x_1,x_2,y_1,y_2,z_1$ and $z_2$ be the unknowns.
How can I solve for the unknowns given the following equations?
Note: I know that $x_1=1, x_2=2k-2, y_1=2k-1, y_2=2k^2-4k+1,z_1=2k-1$ and $z_2=2k^2-4k+2$ is a solution for the system of equation. Unfortunately I cant show how to arrive on it. I think I am missing some steps on showing what I want to show.
My attempt is this:
First using 3,4, and 5 I can express $x_2,y_2$ and $z_2$ in terms of $x_1,y_1$ and $z_1$ and $k$.
Next, I will used the result in first step to change $x_2,y_2$ and $z_2$ in terms of $x_1,y_1$ and $z_1$ and $k$ in equation 2.
Then I will expand 1 and 2 yielding two equations involving $x_1,y_1$ and $z_1$. But after this, I don't know how to proceed and thus I need your help. Thanks a lot.