Write a system of equations:

Let first variable is " y " and second variable is " z ".

Given expression is "The sum of two numbers is 41" and "their difference is 9".

above expression converted in to variables y and z .

"Sum" means addition symbol ()

"Difference" means addition symbol ()

The equation is .

The equation is .

Elimination method:

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

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

When the coefficients of a variable    and are opposites,

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 25 from each side)

                   (Apply additive inverse property: )

                         (Apply additive identity property: )

                                 (Subtract: )

The Numbers are and .