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)}