SOLUTION: Solve the system of linear equations y - z + 2w = 0 3x+2y + w = 0 2x + 4w = 12 -2x -2z + 5w = 6 Do you begin by elinimating x, y z and w in that order?

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Question 48587This question is from textbook College Algebra
: Solve the system of linear equations
y - z + 2w = 0
3x+2y + w = 0
2x + 4w = 12
-2x -2z + 5w = 6
Do you begin by elinimating x, y z and w in that order?
Thank you so very much! This question is from textbook College Algebra

Found 2 solutions by longjonsilver, venugopalramana:
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
you can solve them anyway you fancy.

There are more regimented method using matrix theory... Gaussian Elimination or using determinants, as in Cramer's rule. But for a 4x4 matrix, this will kill you :-D

Good luck lol

Jon

Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
Solve the system of linear equations
y - z + 2w = 0.................I
3x+2y + w = 0................II
2x + 4w = 12............III
-2x -2z + 5w = 6 ..............IV
Do you begin by elinimating x, y z and w in that order?
SINCE EQN.III HAS ONLY X AND W..ELIMINATE Z FROM EQNS.I AND IV AND THEN ELIMINATE Y FROM RESULTING EQN.USING EQN.II..
EQN.I*2-EQN.IV
2Y+2X-W=-6.................................V
EQN.II-EQN.V
X+2W=6....................VI.
EQN.VI*2-EQN.III
0=0.........
HENCE EQNS.ARE DEPENDENT AND CONSISTENT ..THERE WILL BE INFINITE SOLUTIONS.
GIVE ANY VALUE TO X..SAY 0...W=3 FROM EQN.VI
Y=-3/2 FROM EQN.V
GET Z FROM EQN.IV..LIKE THIS YOU CAN GET ANY NUMBER OF SOLUTION.