Thomas invested $8,500 for one year. part of the money was invested at6% and the rest at 9%. the total interest earned was $667.50. how much did thomas invest at the 6% rate?

Okay so say that x=amount invested with 6% and y=amount invested with 9%
x+y=8,500 so > x=8500-y
6%=0.06        9%=0.09
0.06x +0.09y=667.5 (Substitute in x=8500-y so only numbers and y)
0.06(8500-y)+0.09y=667.5 (expand brackets)
510-0.06y+0.09y=667.5 (-510)
0.03y=117.5 (/0.03)
$3916.67=Y  ->9%
X=8500-Y 
x=$4583.33 ->6%