For a certain value of k, the system
x + y + 3z = 10
-4x + 8y + 5z = 7
kx + 2z = 3
has no solutions. What is this value of k?
x + y + 3z = 10 ⇒ -8x -8y -24z = -80 (1)
-4x + 8y + 5z = 7 (2)
kx + 2z = 3 (3)
Add (1) and (2) and we get
-12x - 19z = -73
Multiply (3) by -19/2 and we get
-(19/2)kx -19z = -57/2
We will have no solutions when
-12 = -(19/2)k
k = 2(12) / 19 = 24 / 19
