Alright, Lillian, here we go!
Let d = the cost of a dog and b = the cost of a burger.
3d + 2h = 6.75
2d + 3h = 7
Now, if we add these two equations together, we get 5d + 5h = 13.75. There is something we can do with that to help solve our problem, but I bet it's not what your teacher is looking for.
Instead, we want either d or h to cancel out because we have opposites of either. For example, 15h + (-15h) = 0, right?
Let's cancel out d. If we multiply the top by -2 and the bottom by 3, we'll have 6d and -6d.
-2(3d + 2h) = -2(6.75)
3(2d + 3h) = 3(7)
-6d - 4h = -13.5
6d + 9h = 21
Now, if we add them together, we get 5h = 7.5, so h = 1.5
Let's throw that back into the first equation.
3d + 2(1.5) = 6.75
3d + 3 = 6.75
3d = 3.75
d = 1.25
So, a hamburger costs $1.50 and a hot dog costs $1.25.
Hope this helps!
