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A sporting goods store sells 3 fishing reels and 5 fishing rods for $309. Later, they sell 6 fishing reels and 2 fishing rods for $282 find the price of each item

Answer :

x = reels 
y = rods 
so 
3x + 5y = 309 
6x + 2y = 282 

let's use equation 2 and get the y's on a side by themself by subtracting 6x from both sides 

6x + 2y - 6x = 282 - 6x 
becomes 
2y = 282 - 6x 

now divied both sides by 2 

y = (282 - 6x) / 2 
y = 141 - 3x 
now stick that y value into the first equation 
3x + 5y = 309 
becomes 
3x + 5(141 - 3x) = 309 

multiply it out 

3x + 705 - 15x = 309 
-12x = 309 - 705 
-12x = -396 
x = 33 

cost of each reel = 33 

now substitute 33 for x into equation 1 or equation 2 (it doesn't matter which) to find out the value of each rod using equation 1 
3x + 5y = 309
3(33) + 5y = 309
99 - 309 = -5y
-210 = -5y
y = 42

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