Title: There are three kinds of animals *** 18, including spiders, dragonflies and cicadas, with 1 18 legs and 20 pairs of wings. How many animals are there in each of these three animals? Spiders have eight legs, dragonflies have six legs and two pairs of wings, and cicadas have six legs and a pair of wings.

Solution: There are X spiders, Y dragonflies and Z cicadas.

x+y+z= 18 ( 1)

8x+6y+6z= 1 18 (2)

2y+z=20 (3)

From (3)

z=20-2y

Bring z=20-2y into (1)

x+y+(20-2y)= 18

x+y+20-2y= 18

x-y+20= 18

x-y= 18-20

x-y=-2

x=y-2

Bring z=20-2y and x=y-2 into (2)

8×(y-2)+6y+6×(20-2y)= 1 18

8y- 16+6y+ 120- 12y = 1 18

2y+ 104= 1 18

2y= 1 18- 104

2y= 14

y= 14÷2

y=7

X=y-2=7-2=5。

Z=20-2y=20-2×7=20- 14=6。

That is, x=5, y=7 and z=6.

There are five spiders, seven dragonflies and six cicadas.