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For a certain value of k, the system
x + y + 3z = 10,
-4x + 3y + 6z = 8,
kx + z = 3
has no solutions.  What is this value of k?

 Feb 10, 2022
 #1
avatar+124594 
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x + y + 3z  = 10

-4x + 3y + 6z  = 8

kx + z =  3

 

Strategy :  Eliminate  y

Multiply the first equation by -3  and add to the second.....you should get

 

-7x  -3z  =  -30         (1)

 

Multiply the  third equation by  -3  to match its z term with  (1)  =  - 3kx  - 3z  = -9      (2)

 

So using(1) and (2) we have

 

-7x -3z  =  -30

-3kx - 3z  =  -9

 

We  want to now solve this for k

 

-3kx  = -7x            ....divide through by -x

3k  = 7

k = 7/3 gives  us  no solutions

 

cool cool cool

 Feb 10, 2022

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