trinomial system

Sincd the 3rd equation has only x's and z's, combine the first two equations to get rid of y's:

  -2x + y - z = 2           ---> multiply this equation by 3 --->  -6x + 3y - 3z = 6

   -x -3y + z = -10        ---> leave this equation alone   --->     -x - 3y  + z = -10

                                                                                         ----------------------

                    add down the columns:                                    -7x         -2z = -4

Combine this new equation with the original 3rd equation:

    -7x - 2z = -4            ---> multiply this equation by 3 --->  -21x - 6z = -12

    3x + 6z = -24           ---> leave this equation alone   --->     3x + 6z = -24

                                                                                           ------------------

                      add down the columns:                                    -18x        = -36    -->  x  = 2

Now, replace x with 2 in 3x + 6z = -24, to get the value for z,

and then replace those values into one of the first two original equations to get the value for y.