This is a question from my calculus 3 class.

"Finduandvifandu+ 2v= 3i-k3."u-v=i+j+k

Alright, so I have me a pair of answers but they appear to be different than what the back of the book is telling me they are. I was also given a hint from the teacher that this is linear algebra and that I need to somehow eliminate variables. So I've sort of followed that advise.

The book says:

u= (5/7)i+ (2/7)j+ (1/7)k

v= (8/7)i+ (1/7)j+ (4/7)k

My work however shows similar answers but the constants are wrong. Here is what I did:

To get v:

I multiply (u+ 2v= 3i-k) by -3.

Now I get ( -3u- 6v= -9i+ 0j+ 3k)

I add the other equation 3u-v=i+j+kand get ( -5v= 10i+j+ 4k)

This ends up beingv= -2i- (1/2)j- (4/5)k

To get u:

I multiply ( 3u-v=i+j+k) by -2.

Now I get ( -6u- 2v= -2i- 2j- 2k)

I add the other equationu+ 2v= 3i-kand get ( -5u=i- 2j- 3k)

This ends up beingu= -(1/5)i+ (2/5)j+ (3/5)k

So as you can see, I get different answers. Where did I go wrong and did I even start this problem correctly to begin with?