Different Representation of Linear System Currently working on my Linear Algebra homework and I have come across several problems of the same form that I haven't the slightest clue how to approach.  Keep in mind I haven't taken math classes for some time now, so I am a bit rusty.  I have searched online, and in my book, to no avail.

I certainly don't want anyone to do the problem for me, just (1) what problems of these forms are called - e.g. so I can search on google for info on how to solve it; and (2) maybe some links for where I can get more information.

Sorry for such a stupid post, but I am running short on time, and was hoping someone might be able to help.

One of the problems I'm referring to:
In this case here you have the equations of two planes (in coordinate form). Now you have to get the equation of the intersecting line (parameter form).
Note that you can write the equations in the form
$A \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} 9 \\ 8 \end{bmatrix} -\begin{bmatrix} 5 \\ -3 \end{bmatrix} x_3$, so we get
$\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = A^{-1}\begin{bmatrix} 9 \\ 8 \end{bmatrix} -A^{-1}\begin{bmatrix} 5 \\ -3 \end{bmatrix} x_3$.

In the question you can take $x_3 = s$.