+1887 For a certain value of $k$, the system
x + y + 8z = 10,
x + 5y + 3z = 7 + 7z - 4y,
kx + 2z = 3 - 4y
has no solutions. What is this value of $k$?
+129830 x + y + 8z = 10
x + 9y -4z = 7
kx + 4y +2z = 3
Multiply the second equation by 2
2x + 18y - 8z = 14
add to the first equation
3x + 19y = 24 (1)
Multiply the last equation by 2
2kx + 8y + 4z = 6
add to the second equation
(2k + 1)x + 17y = 13 (2)
Multiply (1) by 17 and (2) by 19
51x + 323y = 408
(38k + 19)x + 323y = 247
This system will have no solution when
38k + 19 = 51
38k = 32
k = 32 / 38 = 16 /19
