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For a certain value of k, the system

\begin{align*}
x + y + 3z &= 10, \\
-4x + 3y + 5z &= 7, \\
kx + z &= 3
\end{align*}
has no solutions. What is this value of k?

 May 22, 2021
edited by Guest  May 22, 2021
 #1
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x  +  y   +   3z    =  10

-4x   +  3y   +  5z  =  7

  kx  +  z  =   3

 

 

Multiply  the  first  equation  through by  -3

 

-3x  - 3y   - 9z  =  - 30

 

Add this  to the second equation  producing

 

-7x   - 4z  =   - 22

 

Multiply the third given equation  through  by   -4   producing

 

-4kx  - 4z  =  -12

 

So   notice  that  if      -7  =  - 4k  ,    k   =   7/4      we eill have  no solutions  because  the  system  then becomes

 

-7x  - 4z  = -22

-7x  -  4z  =  -12         The  left side cannot  simulataneously  give  different results on the right

 

So....no solutions when  k = 7/4

 

cool cool cool

 May 22, 2021

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