SOLUTION: 2x + 3y- z= -16 x + 2y + 2z= -3 -3x + y + z= -5

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Question 906681: 2x + 3y- z= -16
x + 2y + 2z= -3
-3x + y + z= -5

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2x+%2B+3y-+z=+-16 ............1
x+%2B+2y+%2B+2z=+-3 ............2
-3x+%2B+y+%2B+z=+-5 .............3
_________________
2x+%2B+3y-+z=+-16 ............1
x+%2B+2y+%2B+2z=+-3 ............2..multiply by -2
___________________
2x+%2B+3y-+z=+-16+............1
-2x+%2B+2%28-2%29y+%2B+2%28-2%29z=+-3%28-2%29 ............2
___________________
2x+%2B+3y-+z=+-16+............1
-2x+-4y+-4z=+6 ............2.....add both
______________________
2x+%2B+3y-+z+-2x+-4y+-4z=+-16%2B6
+-y+-5z=+-10
10+-5z=+y................1a
now take these two:
x+%2B+2y+%2B+2z=+-3 ............2....multiply by 3
-3x+%2B+y+%2B+z=+-5 .............3
____________________.and add
3x+%2B+6y+%2B+6z%2B%28-3x+%2B+y+%2B+z%29=+-9-5
3x+%2B+6y+%2B+6z-3x+%2B+y+%2B+z=+-14
+7y+%2B+7z++=+-14
7%28y+%2B+z+%29+=+-14
%28y+%2B+z+%29+=+-14%2F7
y+%2B+z+=+-2
y++=+-2-z............1b

use 1a and 1b to calculate z
10+-5z=+y................1a
+-2-z=y............1b
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=>
10+-5z=-2-z
10+%2B2=5z-z
12=4z
highlight%28z=3%29
now find y
-2-z=y
+-2-3=y
highlight%28y=-5%29
and, find x
x+%2B+2y+%2B+2z=+-3 ............2
x+%2B+2%28-5%29+%2B+2%2A3=+-3
x+-10+%2B+6=+-3
x+-4=+-3+
x+=+-3+%2B4
highlight%28x+=+1%29