Elimination method:

Given equations are,

----------(1)

----------(2)

When the coefficients of a variable    and are opposites,

Adding the equations will eliminate the variable.

Adding (1) and (2) equations will eliminate the variable z.

               (Adding (1) and (2) equations)

Apply division property of equality: If a = b then .

                      (Divide each side by 2)

                           (Cancel common terms)

                                (Divide: )

Substitute for y in either equation to find z.

                           (First equation)

                           (Substitute  )

Apply commutative property of addition: .

                 (Subtract 6 from each side)

                      (Apply additive inverse property: )

                            (Apply additive identity property: )

                              (Subtract: )

Check the solution:

To Check, substitute and  in either equation.

                            (First equation)

                            (Substitute and  )

                                  (Subtract: )

The solution  is true.

The solution is .