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For a certain value of $k$, the system x + y + 3z &= 10, \\ -4x + 3y + 5z &= 7, \\ kx + z &= 3 has no solutions, what is this value of $k$

 Apr 8, 2021
 #1
avatar+118626 
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x + y + 3z  =  10

-4x + 3y + 5z  = 7

kx + z  =  3

 

Multiply  the first wquation through by  -3  and we  have

 

-3x -3t - 9z  = -30      add this to the second equation  and we  have that

 

-7x -4z  = -22      (4)

 

Multiply  the  last equation  through by  -4 and we  get

 

-4kx  - 4z  = -12     (5)

 

Lokking at (4)  and (5)..... this will have  no  solution  if

 

-4k  = -7       

 

k  =  -7/ -4

 

k  =7/4

 

cool cool cool

 Apr 8, 2021
 #2
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you made a mistake, in (4) you should have gotten -23 on the right not -22.

Guest Apr 8, 2021

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