SOLUTION: Three solutions to the equation Ax-By-Cz-5=0 are (2,4,-1),(3,6,-2), and(-2,-9,-4). Find C.

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Question 163437This question is from textbook College Algebra
: Three solutions to the equation Ax-By-Cz-5=0 are (2,4,-1),(3,6,-2), and(-2,-9,-4). Find C. This question is from textbook College Algebra

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Three solutions to the equation Ax-By-Cz-5=0 are (2,4,-1),(3,6,-2), and(-2,-9,-4). Find C.

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:

system%282A-4B%2BC=5%2C+3A-6B%2B2C=5%2C+-2A%2B9B%2B4C=5%29

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

matrix%281%2C5%2C+++A=19+%2C+%22%2C%22+%2C++B=7+%2C+%22%2C%22%2C+C=-5%29

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

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

To check, the equation 

Ax-By-Cz-5=0

becomes

%2819%29x-%287%29y-%28-5%29z-5=0

19x-7y%2B5z-5=0

Check to see if (2,4,-1) is a solution to
19x-7y%2B5z-5=0:

19%282%29-7%284%29%2B5%28-1%29-5=0
38-28-5-5=0
0=0

Check to see if (3,6,-2) is a solution to
19x-7y%2B5z-5=0:

19%283%29-7%286%29%2B5%28-2%29-5=0
57-42-10-5=0
0=0

Check to see if (-2,-9,-4) is a solution to
19x-7y%2B5z-5=0:

19%28-2%29-7%28-9%29%2B5%28-4%29-5=0
-38%2B63-20-5=0
0=0

So the problem checks.

Edwin