HELP ME WITH THIS MATH EQUATION THNX!?

(1) : 3x - 2y + z = 12

(2) : x + 3y + z = - 4

(3) : 2x + 2y - 4z = 6

You calculate (1) - (2) and you can get the equation (4)

(4) : (3x - 2y + z) - (x + 3y + z) = 12 - (- 4)

(4) : 3x - 2y + z - x - 3y - z = 12 + 4

(4) : 2x - 5y = 16

(4) : 2x = 5y + 16

(4) : x = (5y + 16)/2

You calculate [4 * (1)] + (3)

4.(3x - 2y + z) + (2x + 2y - 4z) = (4 * 12) + 6

12x - 8y + 4z + 2x + 2y - 4z = 48 + 6

14x - 6y = 54 → recall (4): x = (5y + 16)/2

[14.(5y + 16)/2] - 6y = 54

7.(5y + 16) - 6y = 54

35y + 112 - 6y = 54

29y = - 58

→ y = - 2

Recall (4): x = (5y + 16)/2

x = (- 10 + 16)/2

→ x = 3

Recall (2): x + 3y + z = - 4

z = - 4 - x - 3y

z = - 4 - 3 + 6

→ z = - 1

Add 1 and 3

5x - 3z = 18

2x + 6y + 2z = - 8

-6x - 6y + 12z = - 18____ADD

-4x + 14z = - 26

5x - 3z = 18

-4x + 14z = - 26

20x - 12z = 72

-20x + 70z = - 130_____ADD

58z = - 58

z = - 1

5x = 15

x = 3

3 + 3y - 1 = - 4

3y = - 6

y = - 2

x = 3 , y = - 2 , z = - 1

3x - 2y + z = 12 .....................(1)

X + 3y + z = -4 ...................(2)

2x + 2y - 4z = 6...............(3)

Eliminate any one say x .

This is done by multiplying eqn 2 by 2 and subtract eqn 3

6y+2z-2y+4z= -8-6

4y+6z=-14................................(4)

Similarly subtract 3 times eqn (2) by (1)

-2y+z-9y-3z=12+12

-11y-2z=24.........................(5)

Solve eqn 4 and 5, multiply 4 by 11 and 5 by 4 and add

44y+66z-44y-8z=-154+96

66z-8z=-154+96

58z= -58

Z=-1

-11y-2(-1)=24

-11y=22

Y=-2

Eqn 1

3x+4-1=12

X=3

X=3, y=-1, z=-1

Manipulate first expression to equal z

substitute in the second and third expressions to eliminate z

solve as simultaneous equations in usual way.