Answer: the system of linear equations to represent this scenario are
8x + 4y = 40
3x + 10y = 32
Step-by-step explanation:
Let x represent the cost of one hamburger.
Let y represent the cost of one hotdog.
You spend $40 for 8 hamburgers and 4 hotdogs at a ballgame. This means that
8x + 4y = 40 - - - - - - - - - - - - 1
The next game you spend $32 for 3 hamburgers and 10 hotdogs. This means that
3x + 10y = 32- - - - - - - - - - - - 2
Multiplying equation 1 by 3 and equation 2 by 8, it becomes
24x + 12y = 120
24x + 80y = 256
- 68y = - 136
y = - 136 /- 68
y = 2
Substituting y = 2 into equation 2, it becomes
3x + 10y = 32
3x + 10 × 2 = 32
3x = 32 - 20 = 12
x = 12/3 = 4
