For a certain value of k, the system
x + y + 3z = 10,
-4x + 3y + 6z = 8,
kx + z = 3
has no solutions. What is this value of k?
+130071 x + y + 3z = 10
-4x + 3y + 6z = 8
kx + z = 3
Strategy : Eliminate y
Multiply the first equation by -3 and add to the second.....you should get
-7x -3z = -30 (1)
Multiply the third equation by -3 to match its z term with (1) = - 3kx - 3z = -9 (2)
So using(1) and (2) we have
-7x -3z = -30
-3kx - 3z = -9
We want to now solve this for k
-3kx = -7x ....divide through by -x
3k = 7
k = 7/3 gives us no solutions
