Question 379084
the cost of admission to the spring carnival was $50 for a group of 9 children and 2 adults.
 the admission was $61 for another group of 10 children and 3 adults.
 what was the admission price for each child?
what was the admission price for each adult? 
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I would write it like this (but your way is OK too)
9c + 2a = 50
10c + 3a = 61
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To use elimination, multiply the 1st equation by 3, the 2nd equation by 2:
27c + 6a = 150
20c + 6a = 122
----------------Subtraction eliminates a, find c
7c = 28
c = {{{28/7}}}
c = $4 for children
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Use the 1st original equation to find a, replace c with 4
9c + 2a = 50
9(4) + 2a = 50
36 + 2a = 50
2a = 50 - 36
2a = 14
a = {{{14/2}}}
a = $7 for adults
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We can check these solutions in the 2nd original equation
10c + 3a = 61
10(4) + 3(7) = 61
40 + 21 = 61, confirms our solution
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How about this, did it make sense to you now?