Then the total number x+y+z = 2 1.

Number of legs 8x+6y+6z = 138.

Wing logarithm 2y+z = 23

Solve the ternary linear equations, and get

x = 6，y = 8，z = 7

Suppose there are only a, b and c spiders, dragonflies and cicadas, then

Insect * * * 21:a+b+c = 21(1)

138 leg: 8a+6b+6c= 138, that is, 4a+3b+3c=69 (2)

23 pairs of wings: 2b+c=23 (3)

If a, 4 * (a+b+c)-(4a+3b+3c) = 21* 4-69 is eliminated from 4*( 1)-(2), that is, b+c= 15 (4).

From (3)-(4): (2b+c)-(b+c) = 23-15, that is, b=8.

The results are as follows: c=23-2b=23- 16=7.

a=2 1-a-b=2 1-7-8=6

Among the three kinds of insects, there are 6 spiders, 8 dragonflies and 7 cicadas.

Wish: learning progress!