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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?

 Apr 7, 2023
 #1
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I think the answer is 12/19

 

To get no solutions the variable side must cancel out.

Since the last equation only has variables x and z, we have to cancel the y so

Multiply x+y+3z=10 by 8 to get 8x+8y+24z=80

substract the second equation to get 12x+19z=63

then we have to cancel the z

multiply the last equation by 19 to get 19xz+19z=57

 (12x+19z=63)-(19xk+19z=57) to get 12x-19xk=6

the left side of the equation must equal zero, so 12x=19xk

19k=12

divide by 19

k=12/19

 Apr 7, 2023

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