Heidi bought seven pairs of socks for a total of $18 she bought wool socks and cotton socks the wool socks cost three dollars per pair and the cotton socks cost two dollars per pair X represent the number of pairs of wool socks and Y represent the number of pairs of cotton socks

x = number of pairs of wool socks
y = number of pairs of cotton socks

wool socks = $3 per pair
cotton socks = $2 per pair

Total pairs = 7
⇒ x + y = 7

Total cost = $18
⇒ 3x + 2y = 18

Solve for x and y:

x + y = 7 ------------------ (1)
3x + 2y = 18 ------------- (2)

(1) x 2 : 2x + 2y = 7

 2x + 2y = 14 ------------- (1a)
3x + 2y = 18 ------------- (2)

(2) - (1a):  x = 14

Sub x = 11 into (1):  4 + y = 7
                                 y = 3

x = 4, y = 3

Answer: 4 pairs of wool socks and 3 pairs of cotton socks