SOLUTION: Please help me to solve this equation: x+y+z=2 -x+2y+3z=2 2x-3y-z=1 x-y-z=0

Question 303263: Please help me to solve this equation:
x+y+z=2
-x+2y+3z=2
2x-3y-z=1
x-y-z=0
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
solve this equation:
x + y + z = 2
-x+2y +3z = 2
2x-3y -z = 1
x - y -z = 0
:
Using the 1st and 4th equation
x + y + z = 2
x - y - z = 0
---------------------Addition eliminates y and z, find x
2x = 2
x = 1
:
Use the 2nd and 3rd equation, replace x with 1
-1+2y +3z = 2
2 -3y -z = 1
:
+2y +3z = 2 + 1
3y - z = 1 - 2
:
+2y +3z = 3
3y - z = -1
:
Multiply the above equation by 3, and add to 2y + 3z = 3
9y - 3z = -3
2y + 3z = 3
----------------- addition eliminates z, find y
11y = 0
y = 0
:
Find z using: x + y + z = 2
1 + 0 + z = 2
z = 2 -1
z = 1
:
Summarize x=1, y=0, z=1
:
Check solution in the 2nd equation: -x+2y +3z = 2
-1 + 2(0) + 3(1) =
-1 + 3 = 2

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