At a concession stand five hotd and two hamburgers cost $12.00; two hotdogs and five hamburgers cost 14.25. find the cost of one hotdog and one hamburger

5d + 2h = 12multiply by -2
2d + 5h = 14.25...multiply by 5

-10d - 4h = -24 (result of multiplying by -2)
10d + 25h = 71.25 (result of multiplying by 5)
add
21h = 47.25
h = 47.25 / 21
h = 2.25 <=== each hamburger costs $ 2.25

5d + 2h = 12
5d + 2(2.25) = 12
5d + 4.50 = 12
5d = 12 - 4.50
5d = 7.50
d = 7.50/5
d = 1.50 <== each hot dog costs $ 1.50