Solve the system of equations. (If the system is dependent, enter a general solution in terms of c.
x + 5y - 4z = 22
4x - y + z = 3
5x + 4y - 5z = 35
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Add the 1st and 2nd eqns.
x + 5y - 4z = 22
4x - y + z = 3
----------------------- Add
5x + 4y - 3z = 25
5x + 4y - 5z = 35 ---- eqn 3
-------------------------------------- Subtract
2z = -10
z = -5
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Pick any 2 of the equations.
x + 5y - 4z = 22
4x - y + z = 3
-------
z = -5
x + 5y + 20 = 22
4x - y + -5 = 3
---
x + 5y = 2 times 4 --> 4x + 20y = 8
4x - y = 8
---------
4x + 20y = 8
4x - y = 8
---------------- Subtract
21y = 0
y = 0
x = 2
---> (2,0,-5)