Question 165401
1. 2x+y-3z=-4 
2. 4x-2y+z=9 
3. 3x+5y-3z=5
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Multiply eqn 2 by 3
12x-6y+3z=27
Add to eqn 1 and to eqn 3
1. 2x+y-3z=-4 
 12x-6y+3z=27
 14x-5y = 23  No z term
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3. 3x+5y-3z=5
 12x-6y+3z=27
 15x-y = 32  No z here either
Now there are 2 eqns in 2 unknowns:
14x-5y = 23
15x- y = 32  Multiply this by 5 to get the same y coefficient
75x-5y = 160
14x-5y = 23  Subtract this from it
61x = 137
x = 137/61  Answer for x
Sub x into 15x -y = 32
15*(137/61) - y = 32
y = (15*137 - 32*61)/61
y = 103/61  Answer for y
Sub x and y into any of the 3 original eqns, I'll use #1
1. 2x+y-3z=-4 
2*(137/61) + (103/61) - 3z = -244/61
-3z = (-244 - 274 - 103)/61
-3z = -621/61
z = 207/61