Two cooks purchase plates and cups at the same store. the first cook bought 6 plates and 10 cups for a total of $21.50. the second cook bought 9 plates and 4 cups for a total of $18.50.
what is the price of each type of item purchased?

This is a problem of two equation and two unknowns, 
let x be the price of the plates
and y be the price of the cups

for the first cook, his total purchase price is $ 21.50, in equation form:
6x + 10y = 21.50

for the second cook, his total purchase price is $ 18.50, in eqution
9x  + 4y = 18.50

solve the 2 equations simulataneously
x = $ 1.5 per plate
y = $ 1.25 per cup
are the prices of the two items