Question

At a fast food restaurant, 10 cheeseburgers w/onion and 5 orders of French fries contain 6800 calories. 5 cheeseburgers w/ onion and 3 orders of French fries contain 3590 calories. How many calories are in a cheeseburger w/ onion? How many calories are in one order of French fries?

Answer 1

let's say
c = calories in the cheeseburgers
f = calories in the fries



`\bf \begin{array}{llcll} 10c+5f=6800&\boxed{* -3}\implies &-30c-15f=-20400\\\\ 5c+3f=3590&\boxed{* 5}\implies &25c+15f=17950\\ &&----------\\ &&-5c+0=-2450 \end{array} \\\\\\ c=\cfrac{-2450}{-5}\implies \boxed{c=490}\\\\ -------------------------------\\\\ \textit{now let's plug that in the first equation}\\\\ 10(490)+5f=6800\implies 4900+5f=6800\implies 5f=1900 \\\\\\ f=\cfrac{1900}{5}\implies \boxed{f=380}`

notice, using elimination, the idea for the -3 and 5 multipliers, is to get a -15f atop and 15f at the bottom, thus they "eliminate" the variable "f"