SOLUTION: Solve the system of equations? 4x-4y-z=38 x+4y-3z=6 -3x+2y-z=-14 x=? y=? z=?

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Question 80888: Solve the system of equations?
4x-4y-z=38
x+4y-3z=6
-3x+2y-z=-14
x=?
y=?
z=?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
4x - 4y - z = 38
x + 4y - 3z = 6
-3x+ 2y -z =-14
:
4x - 4y - z = 38
x + 4y - 3z = 6
----------------- adding eliminates y
5x + 06 - 4z = 44
5x - 4z = 44
:
Multiply the 3rd equation by -2 and add to equation 2
x + 4y - 3z = 6
6x - 4y + 2z = 28
------------------ adding eliminates y again
7x + 0y - 1z = 34
7x - z = 34
:
Using the two unknown equations to eliminate z
Multiply 7x - z = 34 by 4 and subtract 5x -4z = 44 from it:
:
28x - 4z = 136
5x - 4z = 44
-----------------
23x + 0z = 92
x = 92/23
x = 4
:
Use 7x - z = 34 to find z, substitute 4 for x
7(4) - z = 34
-z = 34 - 28
-z = 6
z = -6
:
Find y using the 2nd equation x + 4y -3z = 6
4 + 4y - 3(-6) = 6
4 + 4y + 18 = 6
4y + 22 = 6
4y = 6 - 22
4y = -16
y = -16/4
y = -4
:
:
Check solutions in the 1st equation:
4x - 4y - z = 38
4(4) - 4(-4) - (-6) = 38
16 + 16 + 6 = 38