Let us consider the equations are and .

Solve the system of equations by elimination method.

Step 1:

Multiply each equation with a suitable multiplier.

Case (i):

                   (First equation)

         (Multiply each side by )

             (Multiply)

Case (ii):

                   (First equation)

         (Multiply each side by )

               (Multiply)

Step 2:

Subtract the equations to eliminate the one variable.

                   (Divide each side by )

                               (Cancel common terms)

Step 3:

Substitute into any original equation to find value.

                  (First equation)

               (Substitute )

                    (Multiply)

        (Subtract from each side)

                          (Apply additive inverse property: )

                     (Divide each side by )

                              (Cancel common terms)

The solution of the system is .

The solution of the system is .