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

the entire expression should be subtracted from 30. to subtract the quantity, distribute the negative sign, which changes the signs on the terms. so, the –2 changes to positive and gets added to 30 instead of subtracted from it.

hope this ! ^w^

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