Write a system: Gerard bought 9 hamburgers and 3 orders of fries for $24.75. Chris bought 6 hamburgers and 4 orders of fries for $19.50. Each hamburger costs the same amount. Each order of fries costs the same amount. Write a system of linear equations that can be used to find how much one hamburger (h) cost and one order of fries (f) cost. What is the cost, in dollars, for each item?

Starting off with what we know:

Gerard:

9 (h) amburgers + 3 (f) ries = $24.75

Chris:

6 (h) amburgers + 4 (f) ries = $19.50

Now that we have our linear equations, we can focus on one of the variables, or in this case, foods.

For this problem we can set the equations equal to each other if we subtract their totals on both sides like so:

9 (h) amburgers + 3 (f) ries - 24.75 = $24.75 - 24.75

6 (h) amburgers + 4 (f) ries - 19.50 = $19.50 -

19.50

This leaves us with:

9 (h) amburgers + 3 (f) ries - 24.75 = 0

6 (h) amburgers + 4 (f) ries - 19.50 = 0

Now we set them equal to each other:

9 (h) amburgers + 3 (f) ries - 24.75 = 6 (h) amburgers + 4 (f) ries - 19.50

Set either h or f to 0 and solve!