Question 1150775
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Convert the system into an augmented matrix. Then row reduce until the matrix is into Row Echelon Form (REF)


<img src = "https://i.imgur.com/ptJatBC.png">


The last row has nearly all 0's in it except for the last entry that has -3+k


This means we have 
0x + 0y + 0z = -3+k
which is equivalent to
0 = -3+k


Solving for k leads to 
0 = -3+k
-3+k = 0
k+(-3) = 0
k-3 = 0
k-3+3 = 0+3
k = 3


If k = 3, then the equation 0 = -3+k is true. 


So the row 
0x + 0y + 0z = -3+k
will turn into
0x + 0y + 0z = -3+3
0x + 0y + 0z = 0
0 = 0
which is a true statement


If k is anything else but 3, then the equation 0x + 0y + 0z = -3+k will be false and the overall system will be inconsistent.


Final Answer: <font color=red size=4>3</font>
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