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The sum of two positive integers is 35. When the smaller integer is subtracted from twice the larger, the result is 34. Find the two integers. 

 

Let's call the larger number X 

Let's call the smaller number Y 

 

                                                                      X + Y  =  35 

                                                                    2X – Y  =  34 

 

Add the two equations                                       3X  =  69 

Divide both sides by 3                                         X  =  23   the larger number     

 

Plug 23 in place of X in the first equation      23 + Y  =  35 

Subtract 23 from both sides                                  Y  =  35 – 23 

                                                                              Y  =  12   the smaller number 

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