At a concession stand five hot dogs and four hamburgers cost $13.25; four hot dogs and give hamburgers cost $13.75. Find the cost of one hot dog and the cost of one hamburger.

So for this problem lets call hot dogs x and hamburgers y. We know that 5 hot dogs and 4 hamburgers costs $13.25. This can be written as the equation

5x+4y=13.25

Similarly, we know that 4 hotdogs and 5 hamburgers cost $13.75. This gives us the equation

4x+5y=$13.75

Then solve the systems of equations.