Question in Introductory Linear Algebra I really need help with this question. I am in an introductory linear algebra course. If you guys could help me, I would really appreciate it. Here is the question:

A large apartment building is to be built using modular construction
  techniques. The arrangement of apartments on any particular floor is
  to be chosen from one of the three basic floor plans. 
  
  
*
  
*Each floor of
  plan A includes: 3 three bedroom units, 7 two bedroom units and 8 one
  bedroom unit. 
  
*Each floor of plan B includes 4 three bedroom units, 4
  two bedroom units and 8 one bedroom units. 
  
*Each floor of plan C
  includes: 5 three bedroom units 3 two bedroom units and 9 one bedroom
  units.
  
  
  Suppose the building contains a total of $x_1$ floors of plan A,
  $x_2$ floors of plan B, and $x_3$ floors of plan C.   
Is it possible to design
  the building with exactly 66 three bedroom units, 14 two bedroom units
  and 136 one bedroom units?
If it can be done, list two different ways
  to design the building and if not, explain why.


Think about this in the context of a system of linear equations..
Plan A = (3,7,8)
Plan B = (4,4,8)
Plan C = (5,3,9)
Total = (66,14,136)
\begin{bmatrix}
    3 & 4 & 5 & 66 \\
    7 & 4 & 3 & 14 \\
    8 & 8 & 9 & 136 \\
  \end{bmatrix}
Is this system consistent? 
