3x+y-4z=-6
2x+3y-4z=4
x-y+ 2z=-4
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Multiply the 3rd eqn by 2 --> 2x - 2y + 4z = -8
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Add that to the 1st and to the 2nd eqn.
z is eliminated.
You have 2 eqns in x & y.
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3x + y - 4z = -6
2x - 2y + 4z = -8
------------------------------ Add
5x - y = -14 ---- Eqn A
==========================
2x + 3y - 4z = 4
2x - 2y + 4z = -8
------------------------------- Add
4x + y = -4 ---- Eqn B
============================
5x - y = -14 ---- Eqn A
4x + y = -4 ---- Eqn B
-------------------------------- Add
9x = -18
x = -2
=============
4x + y = -4 ---- Eqn B
-8 + y = -4
y = 4
=====================
3x+y-4z=-6 -------- 1st eqn
-6 + 4 - 4z = -6
4z = 4
z = 1
----> (-2,4,1)
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Mathlover used substitution.
I think that takes more work (in this case) than elimination.
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I would use a matrix because I have an Excel sheet that does those, but it doesn't teach anything, just gives the answers.