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For a certain value of k, the system

x + y + 3z = 10

-4x + 8y + 5z = 7

kx + z = 3

has no solutions.  What is this value of k?

 Mar 4, 2023
 #1
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x + y + 3z = 10      →   y =  10 - x - 3z

(we want to get y by itself0

 

-4x + 2y +5z = 7    →   -4x + 2(10 - x - 3z) + 5z = 7   →   -4x + 20 -2x - 6z + 5z  = 7  →  -6x - z = -13  →

 

6x + z  = 13

(substitute y into  the second equation)

 

 

Notice we have this system now 

k*x + z = 3

 

6x + z = 13 

And notice that, if k =6, we would have this system:

 

6x + z  = 3      and

 

6x + z  = 13       but this is impossible, because two things added together can't possibly have two different outcomes 

 

when k = 6, the system has no solution. 

 Mar 5, 2023

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