How to find values of a variable of a plane

[pisces93]

Homework Statement

I am given 3 planes

1) (3-a)x-2y-4z=0
2)-2x-(2+a)y+6z=0
3) 4x+6y-(1+a)z=0

The Attempt at a Solution

So what i did was i expanded the equation

1) 3x-xa-2y-4z=0
2)-2x-27-ya+6z=0
3)4x+6y-z+az=0

and i used the elimination method using

3x-xa-2y-4z=0
-2x-27-ya+6z=0

what i got was a= -10y+10z / 2x-3y

Now i do not know what to do next, i do not even know if i am doing this right can someone help
Thanks!

 

[verty]

What are you trying to do? I think you are trying to find a value of "a" for which there are nontrivial solutions to this system of equations. This is a very difficult question that you have asked, infeasable I think with precalculus math.

I'll look at it some more though.

Hmm, unless you know Linear Algebra, give this one a miss.