Determine what values of a parameter make consistent a given system of linear equations 
Given the system of equations:
  \begin{align*}
x+2ay &= a^2 \\
ax + ay &= a^3+1
\end{align*}
  where $a$ is a constant, determine what values of a make this system of equations consistent. Then, solve the system for one of those values of $a$. 

So I was thinking of putting this into a matrix but I'm a little confused with the variables $a$ and $x$ and $y$. Would I put the a variable into the matrix or no?

Yes, it's convenient to put the system in matrix form, in part because of the following:
Hint An $n \times n$ linear system $A {\bf x} = {\bf b}$ admits a (unique) solution if $\det A \neq 0$.
