Substitute the first solution: (x,y,z)=(2,4,-1) in

Ax-By-Cz-5=0
A(2)-B(4)-C(-1)-5=0
2A-4B+C-5=0
2A-4B+C=5

Substitute the second solution: (x,y,z)=(3,6,-2), in

Ax-By-Cz-5=0
A(3)-B(6)-C(-2)-5=0
3A-6B+2C-5=0
3A-6B+2C=5

Substitute the third solution: (x,y,z)=(-2,-9,-4), in

Ax-By-Cz-5=0
A(-2)-B(-9)-C(-4)-5=0
-2A+9B+4C-5=0
-2A+9B+4C=5

So you have this system of three equations in three
unknowns:



Do you know how to solve that system?  If not post
again.  The solution to that system is 



All you were asked for was C, which is -5.

----------------------------------------

To check, the equation 



becomes





Check to see if (2,4,-1) is a solution to
:





Check to see if (3,6,-2) is a solution to
:





Check to see if (-2,-9,-4) is a solution to
:





So the problem checks.

Edwin