Solve following equation. 4x+8y-4z=4 3x+6y+5z=-13 -2x+y+12z=-17 Please show steps.

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The system of equations to be solved is:

4x + 8y - 4z = 4 ...(1)

3x + 6y + 5z = -13 ...(2)

-2x + y + 12z = -17 ...(3)

(1) + 2*(3)

=> 4x + 8y - 4z - 4x + 2y + 24z = 4 - 34

=> 10y + 20z = -30

=> y + 2z = -3

=> y = -3 - 2z

2*(2) + 3*(3)

=> 6x + 12y + 10z - 6x + 3y + 36z = -26 - 51

=> 15y + 46z = -77

substitute y = -3 - 2z

=> 15(-3 - 2z) + 46z = -77

=> -45 - 30z + 46z = -77

=> 16z = -32

=> z = -2

y = -3 - 2z = -3 + 2*2 = 1

x = 1 - 2y + z

=> 1 - 2 - 2

=> -3

The solution of the system of equations is x = -3, y = 1 and z = -2

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