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A system of equations is given as follows: 1. x+y+2z=1 2. kx+2y+4z=k For what value of k does the system have an infinite number of solutions? Determine the solution to the system for this value of k.

Mathematics
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k=2 will give you two coincident lines, so infinity solutions
yeah, that's my answer too but the book says that "the system will have an infinite number of solutions for \(any\ value\ of\ k\)"
because you have a linear dependent system (2 equations, 3 variables) so, no matter what value of k is, the system has infinite solution set

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AAHhHHH! got it thanks (AGAIN)! :)

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