# system of linear equations question

• Apr 18th 2011, 08:29 PM
fran1942
system of linear equations question
Hello, I have the following set of three linear equations. I am trying to solve for x,y,z using substitution.

x - y - z = 0
-2x + 4y = 0
3y - 2z = 3

My first step is to isolate 'y=z-x'
I then substitute y into the next two equations resulting in:

-3x + 2z = 0
-3x + z = 3

Now when I subtract these I get z = -3, however the answer should be z = 3.
What am I doing wrong here ?

Thanks kindly for any help.
• Apr 18th 2011, 08:30 PM
Prove It
Surely when you subtract the two final equations (which by the way is NOT the substitution method), the x terms are eliminated leaving z = -3...
• Apr 18th 2011, 08:37 PM
fran1942
sorry, my typo. I was meaning z = -3.
The actual answer should be z = 3.

Can you please tell me where I am going wrong. How am I getting z = -3, instead of z = 3 ?

Thanks kindly.
• Apr 18th 2011, 09:43 PM
johnny
-2x + 4y = 0 is equivalent to x - 2y = 0, i.e. x = 2y. Since x - y - z = 0, substitute x = 2y and we get 2y - y - z = y - z = 0, i.e. y = z. Since 3y - 2z = 3, substitute y = z and we get 3z - 2z = z = 3.