A woman bought some large frames for $15 each and some small frames for $6 each. If she bought 13 frames for $114, find out how many of each type she bought

x = small frames

y = large frames

6x+15y = 114

x+y = 13

solve for x

x=13-y

substitute into 6x+15y = 114

6 (13-y) + 15y = 114

distribute

78 - 6y + 15y = 114

combine like terms

78 + 9y = 114

subtract 78 from each side

9y = 36

divide by 9

y = 4

x = 13-y

x = 13-y

x=9

Answer: 9 small frames and 4 large frames