If someone could walk me through the steps, or give me any help at all, that would be great.
Try rewritting this so people can understand it.
If you can't be bothered to learn LaTeX properly treat the subscripts as arguments, so you would write $\displaystyle x_{k+u}$ as $\displaystyle x(k+u) $
Just to rewrite: $\displaystyle x_{k+1}=-5x_k+4y_ky_{k+1}=-12x_k+9y_k$ Is this correct? ("x_k" produces "$\displaystyle x_k$" and "x_{k+1}" produces "$\displaystyle x_{k+1}$" in LaTeX.)