A fast food restaurant sells either small hamburgers or large hamburgers. If one person buys 3 small hamburgers and 5 large hamburgers and spends $33.60, and another person buys 4 small hamburgers and 4 large hamburgers and spends $31.60, calculate how much each burger costs.

Small hamburger: $

Large hamburger: $

First we write a system of equations for this situation, then solve

(3*x* + 5*y* = 33.60) × 4 = 12*x* + 20*y* = 134.4

(4*x* + 4*y* = 31.60) × (-3) = -12*x* – 12*y* = -94.8

12*x* + 20*y* = 134.4

-12*x* – 12*y* = -94.8

--------------------------

8*y* = 39.60

*y* = 4.95

3*x* + 5(4.95) = 33.60

3*x* = 8.85

*x* = 2.95

So each small hamburger costs $2.95 and each large hamburger costs $4.95.