Solution:

y=2/3x ①

2x+8y=22 ②

By (1), have to:

y-2/3x=0 ③

③×8, so:

8y- 16/3x=0 ④

②-④, so:

22/3x=22

x=3

Substitute x=3 into ①, and you get

y=2/3x=2

The solution of this binary linear equation system is: x=3, y=2.

3x+y=7 ①

5x-2y=8 ②

①×2, get

6x+2y= 14 ③

②+③, get

1 1x=22

x=2

Substitute x=2 into ①, and you get

3×2+y=7

y= 1

The solution of this binary linear equation system is: x=2, y= 1.

2x+3y=5 ①

4x-y=3 ②

①×2, get

4x+6y= 10 ③

③-②, yes

7y=7

y= 1

Substitute y= 1 into ① to obtain

2x+3× 1=5

x= 1

∴ The solution of this binary linear equation system is: x= 1, y= 1.

3x-2y=4 ①

5x+3y- 13=0 ②

①×3, get

9x-6y= 12 ③

②×2, get

10x+6y-26=0 ④

③+④, get

19x=38

x=2

Substitute x=2 into ①, and you get

3×2-2y=4

y= 1

The solution of this binary linear equation system is: x=2, y= 1.