Your family goes to a southern style restaurant for dinner. there are 6 total people in your family. some order chicken for $14 and the rest order steak for $17. the total bill is $99. which system could be used to determine the number of chicken dinners (c) and steak dinners (s) ordered?

Define x and y:

Let c be the number of people that ordered chickens.
Let s be the number of people that ordered steak.


Construct the equations:

There are 6  people in all.
c + s = 6

Chicken cost $14 and Steak costs $17. The total bill is $99.
14c + 17s = 99


Solve c and s:

c + s = 6                  (1)
14c + 17s = 99         (2)


From equation 1:

c + s = 6
c = 6 - s


Sub c = 6 - s into equation 2:

14 (6 - s) + 17s = 99
84 - 14s + 17s = 99
84 + 3s = 99
3s = 99 - 84
3s = 15
s = 5


Sub s = 5 into equation 1:

c + s = 6
c + 5 = 6
c = 6 - 5
c = 1


1 person ordered the chicken and 5 people ordered the steak.