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

So substituting in numbers to see if they come near to the amounts
e.g.

if 1 rod is $30 times this b 5 and = $150
$243 - $150 = $93 divided by 2 = $46.50
Using this information then substitute into the other part of the question
6 rods x $30 = $180
8 reels x $46.50 = $372 
372 + 180 = $552 too big

So start again
Choose 35
1 rod is 35 then 5 x 35 = 175
$243 - $175 = $68 divided by 2 = $34
Using this information then substitute into the other part of the question
6 rods x $35 = $210
8 reels x $34 = $272 
210 + 272 = $482 too small

So choose number nearer to 30 so went for 31

31 x 5 = 155
243 - 155 = 88
88 divided by 2 = 44
So (2 x 44) + (5 x 31) = 243

So substituted in the numbers to part 2
31 x 6 rods = 186
44 x 8 = 352
186 + 352 = $538

So rods are $31
Reels are $44