Can you help me solve this problem?

Question

The Cookie Club sold giant cookies and humongous cupcakes for a fund raiser. On the first day, they sold 46 cookies and 18 cupcakes for $182. On the second day, they sold 30 cookies and 26 cupcakes for $190. How much did the Cookie Club sell each cookie and cupcake for?

Answer 1

46H + 18C = 182

30H + 26C = 190

reduce them by 2

23H + 9C = 91

15H + 13C = 95

multiply 1st by 13, 2nd by 9 and subtract to eliminate one variable

299H + 117C = 1183

135H + 117C = 855

164H = 328

H = 328/164 = 2

C = (91-23(2))/9 = (91-46)/9 = 45/9 = 5

a giant cookie went for $2

a cupcake for $5