Math Investigations II

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For what value of k will the system be dependent?
x+3y+2z=-4
3x+4y-z=2
3x-y-8z=k

I'm confused as to what exactly it's asking for by a dependent system. I know this is a system with infinite solutions, but I don't know how to find that in 3 dimensions.

  • Math Investigations II -

    If one equation is just a multiple of another one, then the two are equations are dependent

    Any row manipulations normally used are allowed

    (2)-(3): 5y+7z = 2-k
    (3*1)-(2): 5y+7z = -14

    So, if 2-k = -14, the system is dependent

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