You own a hamburger franchise and are planning to shut down

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 14 bread rolls, 19 defrosted beef patties, and 16 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bread roll, double cheeseburgers each require 2 beef patties, 1 bread roll, and 2 slices of cheese, while regular cheeseburgers each require 1 beef patty, 1 bread roll, and 1 slice of cheese. You want to know how many of each should you make. This problem is about setting up a system of equations. Let x be the number of plain burgers you make; y be the number of double cheeseburgers you make; and z be the number of regular cheeseburgers you make. Write a system of equations to reflect how many of each type you can make. (Place the coefficients in their proper place next to the variables.) You do not need to solve the system.

Solution

x ---> plain burgers

y ----> double cheesebyrgers

z -----> regular burgers

As per information find bread rolls in each items above

Bread rolls: x*1 + y*1+ z*1 = 14

Beaf patties: x*1 + y*2 + z = 19

Opened Cheese slices : x*0 + y*2 + z*1 = 16

So, x+ y + z=14

x +2y +z = 19

0x+ 2y +z = 16