SOLUTION: Using the elimination method, solve the system. x-y+z=-6 2x-y+2z=9 x+y-3z=4

Question 184143: Using the elimination method, solve the system.
x-y+z=-6
2x-y+2z=9
x+y-3z=4
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Using the elimination method, solve the system.
x - y + z =-6
2x - y +2z = 9
x + y -3z = 4
:
Add equations 1 & 3
x - y + z =-6
x + y -3z = 4
------------------eliminates y
2x - 2z = -2
Simplify, divide by 2
x - z = -1
:
Add equations 2 & 3
2x - y +2z = 9
x + y -3z = 4
-----------------eliminates y again
3x - z = 13
:
Using these two 2 unknown equations
3x -z = 13
x - z = -1
--------------subtractions eliminates z, find x
2x = 14
x = 14/2
x = 7
:
Using x - z = -1, find z
7 - z = -1
-z = -1 - 7
-z = -8
z = 8
:
Find y using the 1st equation, substitute for x and z
x - y + z =-6
7 - y + 8 = -6
15 - y = -6
-y = -6 - 15
-y = -21
y = 21
:
you can check solutions in the 2nd or 3rd equations

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