+0  
 
0
9
1
avatar+1351 

For a certain value of k, the system

x + y + 3z = 10 - x + 5y, 
4x + 2y + 5z = 7 + 11y + 19z, 
kx + z = 3 + 5y
has no solutions. What is this value of k?

 Mar 27, 2024
 #1
avatar+128794 
+1

2x  -4y + 3z  = 10

4x - 9y - 14z = 7

kx + 5y + z  =  3

 

The system will have no solution  when  the matrix discriminant  =   0

 

2    -4     3      2      -4

4   -9     -14    4      -9

k    5      1      k        5

 

[ 2*-9 * 1   + -4*-14 * k + 3*4*5 ] - [ k* -9 * 3 + 5 *-14*2 + 1*4 *-4 ]   =   0

 

[-18 + 56k + 60 ] - [ -27k - 140 - 16 ]  =  0

 

83k + 198  = 0

 

k = -198 / 83

 

cool cool cool

 Mar 27, 2024

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