(! ) two cooks purchased plates and cups at the same store. the first cook bought 4 plates and 5 cups for a total of $25.25. the second cook bought 7 plates and 3 cups for a total of $25.50.
what is the price of a plate?

If "a" will be "plate" and "c" will be "cup" it's going to be like this:
4a + 5c = 25.25
7a + 3c = 25.50

Then we multiply first equation by +3 and the second one by -5 the it's going to be like this:
12a + 15c = 75.75
-35a - 15c = -127.5

So we can say:
-23a = -51.75

Then:
a = 2.25
c = 3.25