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?

Hint:
A system is consistent if it has at least one solution.
We know that if the determinant of the coefficient matrix is $\ne 0$ one solution exists, so find when the determinant is null  and you find two values for $a$. 
Test these values in the '' know'' vector $(a^2,a^3+1)^T$. If the vector is null than you have infinitely many solutions. If the vector is not null the the system is inconsistent.
