+2653 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?
+129889 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
