For a certain value of \(k \), the system
\(\begin{align*} x + y + 3z &= 10, \\ -4x + 2y + 5z &= 7, \\ kx + z &= 3 \end{align*}\)
has no solutions. What is this value of \(k \)?
Multiply the first equation by -2 and we have
-2x - 2y - 6z = -20
-4x + 2y + 5z = 7 add these and we get
-6x - z = -13 (1)
kx + z = 3
Multiply (1) by - 1
6x + z = 13
This system will have no solution when k = 6
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