L = price of one lemonade
C = price of one cookie
5L + 2C = 1.5
2L + 5C = 2.7
isolate C:
2C = 1.5 - 5L
C = 0.75 - 2.5L
substitute:
2L + 5(0.75-2.5L) = 2.7
2L + 3.75 - 12.5L = 2.7
-10.5L = -1.05
L = $0.10
plug in:
5(0.10) + 2C = 1.5
2C = 1
C = $0.50
price of one lemonade and one cookie = L+C
0.50+0.10= $0.60