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# 3x-4y=6z-16,4x-y-z=5,x=3y+2 (z-1)[simultaneous equation]

3x-4y=6z-16,4x-y-z=5,x=3y+2 (z-1)[simultaneous equation]

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Rearrange the terms to obtain the general form.

3x-4y-6z = -16 -(1)

4x-y-z = 5    -(2)

x-3y-2z = -2   -(3)

We will eliminate z from the system of equations by multiplying equations (2) and (3) by 6 and 3, respectively. We thus obtain

6∗  (4x-y-z = 5 )

3∗ ( x-3y-2z = -2 )

or

24x-6y-6z = 30 ---------(4)

3x-9y-6z = -6  ----------(5)

Subtracting (1) from (4) we get

24x-6y-6z = 30

-3x  4y  6z =  16

-----------------------

21x-2y = 46 ----------(6)

Subtracting (1) from (5) we get

3x - 9y - 6z = -6

-3x  4y  6z =  16

---------------------------

-5y = 10

y = 10/-5

y = -2

Substituting y = -2 in (6) we get

21x - 2∗(-2) =46

21x + 4 =46

21x = 46-4

21x = 42

x = 42/21

x = 2

Substituting x = 2, y = -2 in equation (1) we get

3∗2-4∗(-2) -6z = -16

6 + 8 - 6z =- 16

14 - 6z = - 16

- 6z = - 16-14

- 6z = -30

z = - 30/-6

z = 5

∴ x = 2, y = -2 z = 5

Solution set = {(2, -2, 5)}