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Answer:

x = -5, y = 4, z = 3

Step-by-step explanation:

(1)   3x +   y  + 3z = -2

(2) 6x + 2y + 9z =  5

(3) -2x -    y  -   z =  3

Step 1. Eliminate one of the variables in two of the equations

6x + 2y + 9z =  5     Subtract twice Equation (1)

6x + 2y + 6z = -4     from Equation (2)

               3z =  9

                 z =  3

Step 2. Set up two new equations in two variables

3x + y  + 9 = -2       Substitute z

-2x - y   - 3 =   3      into (1) and (3)

(4)   3x +  y  = -11      Add Equations  

(5) -2x  -  y  =   6     (4) and (5)

      x          =  -5

Step 3. Substitute x and z into one of the original equations

Substitute into (3)

-2(-5) - y - 3 =  3

  10   - y - 3 =  3

    7  - y       =  3

        - y       = -4

          y       =   4  

The solutions are x = -5, y = 4, z = 3.

Check:

(1) 3(-5) + 4 + 3(3) = -2

    -15    + 4 +  9   = -2

                      -2   = -2

(2) 6(-5) + 2(4) + 9(3) = 5

     -30   +   8   + 27   = 5

                             5   = 5

(3) -2(-5) - 4 - 3 = 3

       10    - 4 - 3 = 3

                      3 = 3