SOLUTION: Determine the values of k such that the system of linear equations does not have a unique solution. (Enter your answers as a comma-separated list.) x + y +

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Determine the values of k such that the system of linear equations does not have a unique solution. (Enter your answers as a comma-separated list.) x + y +       Log On


   

Question 658850: Determine the values of k such that the system of linear equations does not have a unique solution. (Enter your answers as a comma-separated list.)


x
+
y
+
kz
=
9

x
+
ky
+
z
=
6

kx
+
y
+
z
=
5
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Add all three equations together. You'll get:
x%2By%2Bkz=9...........1
x%2Bky%2Bz=6............2
kx%2By%2Bz=5.................3
________________________________
x%2Bx%2Bkx%2By%2Bky%2By%2Bkz%2Bz%2Bz=9%2B6%2B5
2x%2B2y%2B2z%2Bkx%2Bky%2Bkz=20
2%28x%2By%2Bz%29%2Bk%28x%2By%2Bz%29=20
%282%2Bk%29%28x%2By%2Bz%29=20....when %282%2Bk%29=0, then %282%2Bk%29%28x%2By%2Bz%29=0, and that will be if k=-2

%282-2%29%28x%2By%2Bz%29=20
0%28x%2By%2Bz%29=20
0%2Ax%2B0%2Ay%2B0%2Az=20+
0=20 which is impossible, meaning there are no solutions, and therefore no unique solutions if highlight%28k=-2%29