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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 ?

 May 30, 2019
 #1
avatar+109357 
+2

x + y + 3z  = 10    multiply through by -2 ⇒  -2x - 2y - 6z = -20  (1)

-4x + 2y + 5z  = 7   (2)

kx + z  = 3  (3)

 

Add equations (1) and (2)  and we get that

 

-6x -z  =  -13   multiply through by -1  ⇒  6x + z = 13   (4)

 

So  we have equations (3) and (4)

 

6x + z  = 13

kx + z  = 3

 

And when k = 6  we have no solutions

 

 

 

cool cool cool

 May 30, 2019
 #2
avatar+11709 
+1

What is this value of k ?

 

laugh

 May 30, 2019

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