+0  
 
0
5
1
avatar+1748 

For a certain value of $k$, the system
x + y + 3z = 10,
x - 2y + 8z = 7,
kx + 5z = 3

has no solutions. What is this value of k?

 May 17, 2024
 #1
avatar+129512 
+1

The system will have no solutions when the determinant =  0

 

1   1   3    1    1

1 -2    8    1  -2

k   0   5    k    0

 

Det  =  [ 1 * -2 * 5   + 1 * 8 * k ] - [ 3*-2 * k  + 5 * 1 * 1 ] =  0

 

[ -10 + 8k ] - [ -6k + 5 ] = 0

 

-15 + 14k =  0

 

14k  =  15

 

k = 15/14

 

cool cool cool

 May 17, 2024

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