Emily has 8 coins in her purse totaling 50 cents. The only kinds of coins she has are nickels and dimes. How many nickels does Emily have?

5x + 10y = 50
x + y = 8

x = 8 - y
5*(8-y) + 10y = 50
40 - 5y + 10y = 50
10y - 5y = 50 - 40
5y = 10
y = 2

x + y = 8
x + 2 = 8
x = 8 - 2
x = 6

She has 6 nickels and 2 dimes