Question

The cost of 3 notebooks and 4 pencils is $8.50. Determine the cost of one notebook and one pencil

Answer 1

Call the notebooks x, and the pencils y. 
3x + 4y = $8.50 and 5x + 8y = $14.50 
Then just solve as simultaneous equations: 
3x + 4y = $8.50 
5x + 8y = $14.50 

5(3x + 4y = 8.5) 
3(5x + 8y = 14.5) 

15x + 20y = 42.5 
15x + 24y = 43.5 

Think: DASS (Different Add, Similar Subtract). 15x appears in both equations so subtract one equation from the other. Eassier to subtract (15x + 20y = 42.5) from (15x + 24y = 43.5) 

(15x + 24y = 43.5) - (15x + 20y = 42.5) = (4y = 1) which means y = 0.25. 

Then substitue into equation : 
15x + 20y = 42.5 
15x + 5 + 42.5 
15x = 42.5 - 5 = 37.5 
15x = 37.5 
x = 2.5 

15x + 24y = 43.5 
15(2.5) + 24(0.25) 
37.5 + 6 = 43.5 

So x (notebooks) are 2.5 ($2.50) each and y (pencils) are 0.25 ($0.25) each.