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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 \(k \)?

 Sep 25, 2018
 #1
avatar+103049 
+1

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

kx + z  = 3

 

This  system will have no solution  when k  =  6

 

 

cool cool cool

 Sep 25, 2018

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