The price of a small sandwich is $13/3.
How to find price of a small sandwich
Let y denote the large sandwich
and x denote the small sandwich
6 large and 3 small sandwiches cost $34
So,
6y + 3x = $34 ----------------1
2large and 6 small sandwiches cost $33
2y + 6x = ---------------------2
Solving equations 1 & 2 simultaneously
6y + 3x = $34 ----------------1
2y + 6x = ---------------------2
Multiply Equation 1 by 2 to make the coefficients of y in both equations the same:
12y + 6x = 68 (multiplied by 2)
subtract Equation 2 from the modified Equation 1 to eliminate y.
(12y + 6x) - (2y + 6x) = 68 - 33
10y = 35
y = 35/10
= $3.5
Substitute y into either Equation 1 or Equation 2.
Let's use Equation 1:
6* 7/2 + 3x = 34
Solve for x:
21 + 3x = 34
3x = 13
x = 13/3
So, the solution to the system of equations is y = $3.5 and x = $13/3.
The price of a small sandwich is $13/3.