Is there a difference between "Linear System of Equations" and "System of linear Equations"? We are translating German math videos to English and stumbled over the fact that there are two translations of "Lineare Gleichungssysteme":


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*Linear System of Equations

*System of linear Equations (e.g. Wikipedia)


From my point of view those describe two different things. A "linear system" and second a "… system" (which does not have to be linear).
But it seems to be used for the same thing. Why? And is it correct?

PS: Here is the translated video with the (recent) title "Linear System of Equations": https://www.youtube.com/watch?v=SPu8dHq_9VA

Another synonym is "Simultaneous linear equations", which would be equivalent with "Linear simultaneous equations". So, linearity describes the equations at the end. However, I would prefer "linear equations" put together for more clarity. 
