+1379 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?
+130071 Simplify as
2x - 4y + 3z = 10
4x - 9y - 14z = 7
kx -5y + z = 3
This will have no solutions when the discriminant = 0 .....so....
2 -4 3 2 -4
4 -9 -14 4 -9 = D = 0
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
[ -78 +56k ] - [ 124 - 27k ] = 0
-202 + 83k = 0
83k = 202
k = 202 / 83
