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?
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
+2653 
