Question 761416
Nickels = x
Dimes = y
x + y = 21...1
5x + 10y = 150...2
Multiply (1) by 10
10x + 10y = 210...3
5x  + 10y = 150...2
Subtract (2) from (3)
 5x       = 60
  x       = 12
Substitute x = 12 into Eq(1)
x + y = 21
12 + y = 21
     y = 21 - 12
     y = 9
So, Kate has 12 nickels and 9 dimes
Hope this helps.
:-)