The system of linear equations are

                                             (Equation 1)

                                      (Equation 2)

                                            (Equation 3)

The leading of coefficient of the first equation is one, you can begin by saving the x at the upper left and eliminating the other x - terms from the first column.So, adding negative one times the first equation to the second equation produces a new second equation.

So, the new system of equations are

                                            (Equation 1)

                                           (Equation 2)

                                            (Equation 3)

Now that all but the first x have been eliminated from the first column, go to back on the second column.(You need to eliminate y from the third equation.)So, adding second equation to the third equation produces a new third equation.

So the new system of equations are

                                            (Equation 1)

                                           (Equation 2)

                                                    (Equation 3)

Finally, you need a coefficient of 1 for y in the second equation and coefficient of 1 for z in the third equation, so multiply the second equation by  produces a new second equation and so multiply the third equation by  produces a new third equation respectively.The new system in row - echelon form of equations are

                                            (Equation 1)

                                             (Equation 2)

                                                        (Equation 3)

To solve for y, the value of substitute in equation 2 to obtain as follows:

                                         (Substitute )

                                            (Add 3 to each side)

                                                     (Apply LCM rule: )

To solve for x, the values of substitute in equation 1 to obtain as follows:

                                        (Substitute )

                                        (Subtract from each side)

                                              (Simplify)

                                                    (Apply LCM rule: )

The solution is , which can be write as the ordered triple .

The solution is .