When six times the larger of two numbers is added to seven times the smaller, the result is 114. Ten times the larger less nine times the smaller is 66. Determine the numbers.

Step-by-step explanation:

Let the larger number = x

Smaller number = y

6x + 7y = 114 (I)

10x - 9y = 66 (II)

Multiply equation (I) by 9 and multiply the equation (II) by 7. After that add the two equations. So that, y will be eliminated and we can find the value of x

         (1)*9        54x + 63y = 1026

         (II)*7        70x - 63y  =  462    {Now add}

                        124x           = 1488   {Divide both sides by 124}

                                        x = 1488/124

x = 12

Plugin x =  12 in any of the equation. Here, We are substituting in  equation (I)

6*12 + 7y = 114

  72 + 7y =114

         7y = 114 - 72

         7y = 42

          y = 42/7

y = 6

The numbers are 12 , 6

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