write systems of equations from context

Question

Christopher went into a restaurant and bought 5 hamburgers and 10 drinks, costing a total of $52.50. Wyatt went into the same restaurant and bought 2 hamburgers and 9 drinks, costing a total of $31. Write a system of equations that could be used to determine the price of each hamburger and the price of each drink.

Answer 1

5H + 10D = 52.50

2H + 9D = 31

multiply 2nd equation by 5, and 1st by 2

10H + 45D = 155

10H + 20D = 105 subtract to eliminate one variable

25D = 50

D =50/25 = $2 for a drink

2H + 9(2) = 31

2H = 31-18 = 13

H = 13/2 = $6.50 for a hamburger