Determine the value of k so that the following system is consistent.find solution for these values of k.

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$[(3w+2x+4y+0z=3),(0w+x+y+z=k),(5w+4x+6y+0z=15)]$. I first used elementary row operation. Then $k$ seems to be taking any value for system to be consistent. I'm not sure of its correct and if it is how do l find for the values of $k$.

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I suggest, with consistent you mean, you search for values for $k$ such that the system has at least one solution. Then you are right. For any $w,x,y, k$ you can choose $z=k-x-y$