Question 48587
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.