I've tried solving this problem for a couple hours and I am stumped

a little help would be much appreciated

X + Y + Z = 18

X - Y - Z = 12

3X - 2Y + 4Z = 4

Thanks in Advanced

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- Jan 31st 2010, 01:13 PMjasimmons86Three-Variable Linear Systems
I've tried solving this problem for a couple hours and I am stumped

a little help would be much appreciated

X + Y + Z = 18

X - Y - Z = 12

3X - 2Y + 4Z = 4

Thanks in Advanced - Jan 31st 2010, 01:21 PMpickslides
You need to solve

You you know how to find this inverse? - Jan 31st 2010, 01:27 PMjasimmons86
i dont know how to find the inverse

- Jan 31st 2010, 01:32 PMpickslides
You can use this Matrix calculator

Assuming you know simple matrix operations like mulitplication and finding determinants,

To solve the system consider cramer's Method.

Cramer's rule - Wikipedia, the free encyclopedia

If you don't know these elementary ideas I suggest this problem should be solved using subtitution and elimination. - Jan 31st 2010, 01:35 PMQuacky
(1) X + Y + Z = 18

(2) X - Y - Z = 12

(3) 3X - 2Y + 4Z = 4

Here's my simplistic and basic method :o

Rearranging (1) to isolate X

(4)

Substituting into (2)

Rearranging this gives:

Taking out (and then dividing through by) a common factor of 2 gives

Substituting this into equation 1 gives

Substituting that into all equations leaves:

Which can then be solved easily simultaneously to give

Then substituting this back into the above equations will give

- Jan 31st 2010, 01:43 PMSoroban
Hello, jasimmons86!

What methods are you allowed to use?

Quote:

Add [1] and [2]: /

. .

Hence: .

Substitute into [3]: .