Question 1145714
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First appearance of the system


    10x + 10y = 20    (1)

     2x + 14y = 13    (2)


Multiply equation (2) by 5 (both sides).  Keep equation (1) as is.

Second appearance of the system


    10x + 10y = 20    (1')

    10x + 70y = 65    (2')


Now subtract equation (1') from equation (2').  The terms "10x" will cancel each other (ELIMINATION !), and you will get


          60y = 45,

            y = {{{45/60}}} = {{{3/4}}} of the dollar = $0.75.


Next substitute y = 0.75 into equation (1') to get

     10x = 20 - 10*0.75 = 12.50,

       x = 1.25.


<U>ANSWER</U>.  The price for each coffee is $1.25;  for each doughnut $0.75.
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