Asupporting goods store sells 2 fishing reels and 5 fishing rods for $243. later, they still 8 fishing reels and 6 fishing rods for $538. find the price of each item.

To answer this, you can set up a system of equations.  Solve for one of the variables and substitute this new equation into the 2nd equation.

2x + 5y = 243 - I'll solve this one for x.
8x + 6y = 538

2x + 5y = 243
2x = 243 - 5y
2          2
x = 121.5 - 2.5y ;  substitute this in for x in the second equation

8x + 6y = 538
8 (121.5 - 2.5y) + 6y = 538
972 - 20y + 6y = 538
972 - 14y = 538
-972            -972
-14y = -434
-14       -14
y = 31

The cost of a rod (y) is $31.  

x = 121.5 - 2.5y
x = 121.5 - 2.5 x 31
x = 44

The cost of a reel(x) is $44.

For this case, the first thing we must do is define variables:
 x: price of fishing reels
 y: price of fishing rods
 We write the system of equations:
 2x + 5y = 243
 8x + 6y = 538
 Solving the system we have:
 x = 44 $
 y = $ 31
 
 the price of each item is:
 x = 44 $
 y = $ 31