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avatar+1911 

For a certain value of $k$, the system
x + y + 8z = 10, 
x + 5y + 3z = 7 + 7z - 4y, 
kx + 2z = 3 - 4y
has no solutions.  What is this value of $k$?

 Mar 8, 2024
 #1
avatar+129881 
+1

x + y + 8z  =  10

x + 9y -4z  =  7

kx + 4y +2z = 3

 

Multiply the second equation  by 2

2x + 18y  - 8z  = 14

add to the first equation

3x + 19y  = 24        (1)

Multiply the last equation by 2

2kx + 8y + 4z  = 6

add to the second equation

(2k + 1)x + 17y = 13    (2)

 

Multiply (1)    by 17    and (2) by 19

 

51x + 323y  = 408

(38k + 19)x + 323y =  247

 

This system will  have no solution  when

 

38k + 19 = 51

38k  = 32

k = 32 / 38  =  16  /19

 

cool cool cool

 Mar 8, 2024

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