At a high school football game jamie buys 6 hot dogs and 4 soft drinks for $13. amy buys 3 hot dogs and 4 soft drinks for $8.50. what is the price of a hot dog?

X=price of a hot dogy=price of a soft drinkWe can suggest the following system of equations:
6x+4y=133x+4y=8.50
We solve this system of equations by reduction method.  6x+4y=13-(3x+4y=8.5)   3x=4.5              ⇒x=4.5/3=1.5
the price of a hot dog will be $1.5.

If you want to know the price of a soft drink, you have to find "y".6x+4y=13
6(1.5)+4y=139+4y=134y=13-94y=4y=4/4y=1
The price of a soft drink is $1. 
Hope this helps! :)