5x - y + z = -6
2x + 7y + 3z = 8
x + 2z = 6

Step-by-step explanation:

The system of equations given are:

 5x - y + z = -6   i

 2x + 7y + 3z = 8   ii

  x + 2z = 6 iii

Let us deal with equation i and ii first since they have 3 variables x, y and z;

      5x - y + z = -6                 x 7

       2x + 7y + 3z = 8            x 1

    35x  - 7y + 7z  = -42    iv

      2x  + 7y + 3z  = 8       v

Add equation iv and v;

    37x + 10z  = -34 vi

So, let us solve equation vi and iii:

               x + 2z = 6 - iii   x 10

               37x + 10z  = -34  --- iv  x 2

    10x + 20z   = 60         vi

     74x + 20z  = -68        vii

Subtract vi  - vii;

      -64x  = 128

          x  = -2

So;    put x  = -2 into iii;

           x + 2z  = 6

           -2 + 2z  = 6

            2z  = 6 + 2  = 8

           z  = 4

Put x  = -2 and z = 4 into equation i;

  5(-2) - y + 4  =  - 6

   -10 -y  +4  = -6

       -6  - y  = -6

             -y  = 0

              y  = 0

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