x+ y+(k −5)z=k where k is an arbitrary constant. For which value(s) of k does this system have a unique solution? For which valu
e(s) of k does the system have infinitely many solutions? For which value(s) of k is the system inconsistent?
1 answer:
Answer: Lets rewrite our equation.
x + y + kz - 5z =k
x + y -5z = k(1-z)
k = 
so the only problem with the equation is that z can't be equal to one.
but x and y are free, so you have two free variables and one equation,
that means that for any k the system has infinitely many solutions.
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