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

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