algebra expression

Question

The sum of two numbers is 63. The sum of the smaller and 7 times the larger is 261. find the two numbers

Answer 1

Step 1) Write two equations

 

x - smaller number

y - larger number

 

x + y = 63

x + 7y = 261

 

Step two use elimination method to solve for one of the variables.

 

(-1) (x + y = 63)  ->  -x - y = -63

                                  x + 7y = 261

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

                                        6y = 198

                                        ---    ----

                                         6       6

                                         y = 33

 

Step 3: Substitute the solution into one of the original two equations

 

  x + y = 63

  x + 33 = 63

     - 33 = -33

 ------------------

        x = 30

 

x = 30

y = 33