Answer :
x - dimes
y - nickels
[tex]0.1x+0.05y=6.6\\ x+y=96\\\\ 0.1x+0.05y=6.6\\ x=96-y\\\\ 0.1(96-y)+0.05y=6.6\\ 9.6-0.1y+0.05y=6.6\\ -0.05y=-3\\ y=60\\\\ x=96-60\\ x=36[/tex]
36 dimes and 60 nickels.
y - nickels
[tex]0.1x+0.05y=6.6\\ x+y=96\\\\ 0.1x+0.05y=6.6\\ x=96-y\\\\ 0.1(96-y)+0.05y=6.6\\ 9.6-0.1y+0.05y=6.6\\ -0.05y=-3\\ y=60\\\\ x=96-60\\ x=36[/tex]
36 dimes and 60 nickels.